PURPOSE: To reduce noise and vibration during operation by composing a sheath with end connecting members, of an inner tubular layer formed of self- lubricating thermoplastic material, and an outer tubular layer formed of thermoplastic rubber in a flexible transmission shaft used for a tachometer or the like for an automobile.

CONSTITUTION: A transmission shaft 1 is composed of a steel wire or cable 2 inserted in a sheath 3, and the sheath 3 is connected to a rotatory-driving member R1 and a rotatory-driven member R2 through end connectors 4, 5. Both ends of the cable 2 are fixed to the rotatory-driving member R1 and directly to the rotatory-driven member R2 through intermediate connecting members 6 respectively with torsional elasticity. The sheath 3 is composed of an inner tubular layer 7 generally formed of self-lubricating thermoplastic material such as polyamide with graphite filled, and an outer tubular layer 8 formed of thermoplastic rubber.