Bicycle with rear suspension and relative system of transmissions

A bicycle comprising a frame, a rear wheel, a suspension system of the rear wheel with respect to the frame that allows a predetermined relative displacement between them, a drivetrain system for transmitting the motion from a crankset to the rear wheel, where the drivetrain system comprises a crankset fixed to the frame, a hub and pinion assembly fixed to the rear wheel that is rotatable about a common pivot axis thereof, and a drive chain placed to connect the crankshaft and the hub and pinion assembly directly to each other, where the crankset and the hub and pinion assembly are subjected to reciprocal displacement by the action of the suspension system, where at least one among the crankset and the hub and pinion assembly comprises a free stroke device placed to allow both a forward and backward free angular stroke of the chain with respect to the respective pivot axes of the crankset and/or of the hub and pinion assembly, where the angular stroke is limited by a predetermined angle of entity related to said relative movement between wheel and frame, wherein the forward stroke is the one that occurs both in the passage from an extended position to a compressed position of the suspension, and at the start of the pedalling in extended position of the suspension, said free stroke device comprises first damper means that act for the entire forward angular stroke, opposing the forward angular stroke, and said free stroke device comprises additional damper means that act only in a final stretch of the forward angular stroke, opposing final stretch of the forward angular stroke.