  We study the applicability of collisional models for non-Markovian dynamics
of open quantum systems. By allowing interactions between the separate
environmental degrees of freedom in between collisions we are able to construct
a collision model that allows to study quantum memory effects in open system
dynamics. We also discuss the possibility to embed non-Markovian collision
model dynamics into Markovian collision model dynamics in an extended state
space. As a concrete example we show how using the proposed class of collision
models we can discretely model non- Markovian amplitude damping of a qubit. In
the time-continuous limit, we obtain the well-known results for spontaneous
decay of a two level system in to a structured zero-temperature reservoir
