ATEL Capital Equipment Fund VIII, LLC

                          Supplement dated May 31, 1999
                    to the Prospectus dated December 7, 1998
                    of ATEL Capital Equipment Fund VIII, LLC
                                  (the "Fund")
        (to be used in conjunction with supplement dated April 30, 1999)


The  Fund's  Prospectus  is hereby  supplemented  as set forth on the  following
pages.  This  supplement  is a part of and  must be  accompanied  by the  Fund's
Prospectus dated December 7, 1998.  Terms not otherwise  defined herein have the
meaning as defined in the Prospectus.

Equipment Acquisitions

Set forth below is a summary of the Equipment  acquisitions  and leases  entered
into or identified by the Fund as of the date of this supplement.

                             EQUIPMENT ACQUISITIONS




                                                 Equipment         Commence      Acquisition       Indebt-    Lease    Lease
                          Lessee                    Type         Date(s) (1)      Price (2)       edness (3) Term (4) Type (5) Notes
                          ------                    ----         -----------      ---------       ---------- -------- -------- -----

Leases Funded:
                                                                                                          
BJ's Wholesale Club, Inc.       Forklifts                           Apr-99            $ 594,748         $ -     60      HP
Consolidated Diesel             Telephone System                    Feb-99              406,030           -     55      HP
   Company
General Electric Company        Machining centers                   Mar-99              352,000           -     84      HP     (6)
General Electric Company        Extruder systems                    May-99              281,595           -     60      OL     (7)
General Electric Company        Machining centers                   May-99              670,672           -     84      HP     (6)
General Electric Company        Machining centers                   Aug-99              223,509           -     84      HP     (6)
General Electric Company        Radiographic Inspection Facility    Jun-99               43,875           -     84      HP     (6)
Omnicom Group, Inc.             Office Automation                   Oct-98            1,749,913           -     36      HP
Omnicom Group, Inc.             Office Furniture                    Oct-98              321,976           -     60      FP
Overnite Transportation         Conventional Tractors               Apr-99            2,080,400           -     48      OL
   Company
Sebastiani Vineyards, Inc.      Bottle Filler                       Jul-99               98,237           -     84      FP
Southwest Airlines Company      Boeing 737 Aircraft                 Mar-99            3,238,500           -     50      OL
Staples, Inc.                   Point of sale                       Jan-99            2,410,939           -     60      FP
Staples, Inc.                   Point of sale                       Apr-99              681,910           -     60      FP
TASC, Inc.                      Office Automation                   Jul-99              110,036           -     36      FP
Transamerica Leasing, Inc.      Intermodal Containers               Dec-98            8,500,000           -     120     FP
Universal City Development      Point of sale                       Apr-99              668,474           -     60      FP
   Partners
Universal City Development      Office Automation                   Jul-99              289,072           -     36      FP
   Partners
Williams Distributed            Micro Turbine Systems               May-99              280,500           -     60      HP     (8)
   Power Services, Inc.
                                                                               ----------------- -----------
                    Total funded as of May 31, 1999:                                 23,002,386           -
                                                                               ----------------- -----------

Leases Committed:
General Electric Company        Manufacturing                    May-99 to Oct-99     1,690,318           -     84      HP     (6)
General Electric Company        Manufacturing                    May-99 to Oct-99       211,092           -     84      HP     (6)
General Electric Company        Manufacturing                    May-99 to Aug-99     2,747,940           -     84      HP     (6)
General Electric Company        Manufacturing                    May-99 to Jul-99       218,405           -     60      OL     (7)
General Electric Company        Manufacturing                    May-99 to Jul-99       175,502           -     84      HP     (6)
Sebastiani Vineyards, Inc.      Food Processing                     Jun-99              254,647           -     84      HP
TASC, Inc.                      Office Automation                May-99 to Oct-99       693,469           -     36      FP
Universal City Development      Point of Sale Equipment          May-99 to Jul-99       144,021           -     60      FP
   Partners
Universal City Florida          Office Automation                May-99 to Oct-99       846,619           -     36      HP
   Partners
Williams Distributed            Micro Turbine Systems               May-99            3,544,500           -     60      HP     (8)
   Power Services, Inc.
                                                                               ----------------- -----------
                    Total committed as of May 31, 1999:                              10,526,513           -
                                                                               ----------------- -----------
                    Total Acquisition Price:                                       $ 33,528,899         $ -
                                                                               ================= ===========

                           NOTES

(1) In many cases, a Lease transaction is funded over a period of time according
to the Lessee's requirements. Therefore, "Commence Date(s)" expressed as a range
represents  multiple Lease commencement dates occurring or anticipated under the
same Lease line.



(2) "Acquisition Price" includes either amounts committed to Lessees for funding
by the Program, or actual Equipment  acquisition costs as of April 30, 1999. All
figures are rounded to the nearest dollar.  For any  transactions  which are not
fully  funded,  the  "Acquisition  Price"  may  change  as a result  of  ongoing
fundings.  To  the  extent  that  the  transaction  is  not  fully  funded,  the
information in the table  represents the Managing  Member's best estimates as to
the size,  timing and terms of the transaction  upon full funding,  based on the
outstanding lease commitment,  its discussions with the lessee,  the current and
anticipated  availability  of Fund  capital and other  factors.  There can be no
assurance,  however,  that the  portion  of the  transaction  which has not been
funded will be completed as described.

(3)  "Indebtedness"  is the original  principal  amount of the debt  acquired or
assumed  by the  Fund in  order  to  acquire  the  Equipment  and  leverage  the
Acquisition  Price of the  Equipment.  Although  transactions  may originally be
purchased for all cash, the Managing Member may subsequently  leverage equipment
in order to achieve an overall debt-equity balance for the portfolio.

(4) "Lease Term" is expressed  in terms of months,  although  actual Lease Terms
may be monthly, quarterly, semiannual or annual.

(5) A designation  of "FP"  indicates  that the  aggregate  rents to be received
during the Lease Term equal or exceed the Acquisition Price of the Equipment.  A
designation of "HP" indicates that the aggregate rents to be received during the
Lease Term  equal or exceed 90% of the  Acquisition  Price of the  Equipment.  A
designation of "OL" indicates that the aggregate rents to be received during the
Lease Term are less than 90% of the Acquisition Price of the Equipment.

(6) Lessee is GE Aircraft Engines.

(7) Lessee is GE Plastics.

(8) Guaranteed by Williams Holdings of Delaware, Inc.