The method of nonequilibrium statistical operators developed by Zubarev (1974) has been extended to study transient hot-electron transport in many-valley semiconductors. A set of coupled evolution equations with memory effect are derived to determine the time-dependent drift velocities upsilon _alpha(t), hot-electron temperatures T_alpha(t) and populations N_alpha(t) of various valleys under time-dependent electric fields. In the classical approximation these nonlinear differential equations are applied to study the transient transport of GaAs with a Gamma -L-X band structure under electric fields with several configurations: (i) time-step; (ii) rectangular time pulse; (iii) high-frequency sinusoid. Using the same set of parameters, the authors' calculated results for upsilon _d(t)= Sigma _alphaN_alpha(t) upsilon _alpha(t)/ Sigma _alphaN_alpha(t) compare quantitatively with those in Monte Carlo calculations.