Recently, a type II ARQ scheme using convolutional coding has been analyzed over a nonstationary channel. It has been shown that the type II ARQ scheme performs very well on this type of channel. In this paper we analyze a generalized type II ARQ scheme using punctured convolutional coding on a two-state Markov model of a nonstationary channel. A simple ARQ scheme with memory is also analyzed. It is shown that the simple memory ARQ scheme offers a substantial throughput improvement over a conventional ARQ scheme at severe channel conditions. Furthermore, it is shown that the generalized type II ARQ scheme yields a better performance than the conventional type II ARQ scheme under all channel conditions, thus making it attractive for use over time-varying channels.