<p>We give a substitute to the Feller property for semigroups of time-changed processes; under some conditions this leads to sufficient (new) conditions for the semigroups to be Feller. Moreover, given a standard process and a sequence of measures converging vaguely to a final measure, under some assumptions, we establish convergence of the sequence of the semigroups and the resolvents of the corresponding time changed-processes. Some applications are given: convergence of solutions of evolution equations and convergence of finite time distributions, as well as weak convergence of the related processes.</p>