It is shown that equations of motion for mean values of operators deri
ved from the time-convolution (time-convolutionless) generalized maste
r equation for the density matrix and from the equations for operators
from the Mori (Tokuyama-Mori) theory are the same, provided that proj
ectors are suitably chosen. This is valid also for systems described b
y time-dependent Hamiltonians, We can emphasize that the equivalence o
f the corresponding equations remains valid when invoking approximatio
ns.