To investigate the deformation properties of TiC-(5-20) mol% Mo solid solution single crystals at high temperature by compression testing, single crystals of various compositions were grown by the radio frequency floating zone technique and were deformed by compression at temperature from 1250K to 2270K at strain rates from $5.1{ imes}10^{-5}$ to $5.9{ imes}10^{-3}/s$. The plastic flow property of solid solution single crystals was found to be clearly different among a three-temperature range (low, intermediate and high temperature ranges) whose boundaries were dependent on the strain rate. From the observed property, we conclude that the deformation in the low temperature range is controlled by the Peierls mechanism, in the intermediate temperature range by the dynamic strain aging and in the high temperature range by the solute atmosphere dragging mechanism. The work softening tends to become less evident with an increasing experimental temperature and with a decreasing strain rate. The temperature and strain rate dependence of the critical resolved shear stress is the strongest in the high temperature range. The curves are divided into three parts with different slopes by a transition temperature. The critical resolved shear stress (${ au}_{0.2}$) at the high temperature range showed that Mo content dependence of ${ au}_{0.2}$ with temperature and the dependence is very marked at lower temperature. In the higher temperature range, ${ au}_{0.2}$ increases monotonously with an increasing Mo content.