A clutch arrangement in a transmission, particularly in an automatic transmission or automated selector transmission in the design of a double clutch transmission, having two axially and radially adjacent multi-disc clutches (B, E) in which an inner discs (23) of the radially inner clutch (E) are situated upon an inner disc carrier (37) and an outer discs (21) of the radially outer clutch (B) upon an outer disc carrier (38) while an inner discs (22) of the radially outer clutch (B) and an outer discs (24) of the radially inner clutch (E) are situated upon a common disc carrier (9). It is further provided that discs (23, 24) of radially inner disc set (40) axially support themselves against a guard ring (16) fastened on the common disc carrier (9). To achieve a clutch arrangement that spares space and is economical, it is proposed that the discs (21, 22) of a radially outer disc set (39) can be axially pressed against a contact section (7) of the common disc carrier (9) which consists of a radially outwardly pointing end piece of the common disc carrier (9).