The clamping system comprises a collar (10) having a band (12) that has two flanks (13A, 13B), between which an inside trough (14) is defined that receives projecting clamping surfaces (1A, 2A) of two tubes (1, 2) to be assembled together. The system further comprises a plurality of individual retaining clips (20) distributed angularly around the first flank (13A), each clip having an inside branch (30) and an outside branch (32) facing each other, and between which the first flank is pinched, and a retaining portion (34) that, in the pre-attached state, is suitable for co-operating with the clamping surface (1A) of the first tube (1), one of the branches carrying a first bearing zone (36) that co-operates with a first bearing surface (13′A) of the collar that faces towards the axis (A) of said collar.