The usual development of the continuous-time random walk (CTRW) proceeds by assuming that the present is one of the jumping times. Under this restrictive assumption integral equations for the propagator and mean escape times have been derived. We generalize these results to the case when the present is an arbitrary time by recourse to renewal theory. The case of Erlang distributed times is analyzed in detail. Several concrete examples are considered. Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.