Filed Under Rule 424 (b)(3)
                             Registration Statement No. 333-18367

    SUPPLEMENT NO.  34  TO PROSPECTUS DATED JANUARY 3, 1997
               (AS SUPPLEMENTED JANUARY 10, 1997)


AT&T CAPITAL CORPORATION


Medium Term Notes, Series 4


Due Nine Months or More From Date of Issue.

Issue Price: 100%
  (as a percent of principal amount)


Floating Rate Notes
- -----------------------

Interest Rate Per Annum.......Float%

SETTLEMENT DATE:              12/09/97
INITIAL PAYMENT DATE:         01/09/98
MATURITY DATE:           12/09/98
DAYCOUNT:                ACTUAL/360
INDEX:                   1 Month LIBOR + 0.24%
SOURCE:                  TELERATE PAGE 3750
RESET FREQUENCY:              Monthly
PAYMENT FREQUENCY:       Monthly
PAYMENT:                 Monthly, Pays the 9TH or next Good
Business
                              Day of each Month. Commencing
01/09/98
INTEREST DETERMINATION:       Monthly Reset, Paid
                              Monthly - Source: Telerate p. 3750.
2 London
                              Business Days Prior to Each Reset
Date.
REDEMPTION:                   Non-Call Life
AMOUNT OF SALE:               $10,000,000.00
CUSIP NUMBER:            00206HG32


Date of Sale: December 5, 1997