  We consider a generational and continuous-time two-phase model of the cell
cycle. The first model is given by a stochastic operator, and the second by a
piecewise deterministic Markov process. In the second case we also introduce a
stochastic semigroup which describes the evolution of densities of the process.
We study long-time behaviour of these models. In particular we prove theorems
on asymptotic stability and sweeping. We also show the relations between both
models.
