Induction periods of self-decomposition of anoxic acetylene diluted by a propane-butane mixture or hydrogen were measured experimentally behind incident and reflected shock waves. A source of the shock wave was provided by a detonation wave that was initiated in a stoichiometric acetylene-oxygen mixture, and then changed to the shock wave in investigated mixtures of acetylene with admixtures. Produced shock waves had an intensity 3.0-9.0 MPa at duration 100-1000 μs. Dependence of the induction period of detonation of acetylene on temperature behind the incident/reflected shock wave was presented. Induction periods were obtained for the acetylene mixtures undiluted by inert gases at initial pressures 0.1 MPa and 0.25 MPa, and degrees of compression 10-20. It was shown that the induction period has a minimal value at a non-zero concentration of admixture.