In this paper the model of the generalized thermoelasticity with phase-lags in a perfectly conducting an infinitely long solid cylinder with variable thermal conductivity is established. The surface of the cylinder is traction free and subjected to time dependent temperature. A detailed analysis of the effects of phase-lags, the angular frequency of thermal vibration and the variability thermal conductivity parameter on the displacement, incremental temperature, and the thermal stresses are presented. Comparisons are also made with the results predicted by the coupled theory and with the theory of generalized thermoelasticity with one relaxation time. Finally, some of the earlier results are deduced as particular cases.