  A random walk scheme, consisting of alternating phases of regular Brownian
motion and L\'evy walks, is proposed as a model for run-and-tumble bacterial
motion. Within the continuous-time random walk approach we obtain the long-time
and short-time behavior of the mean squared displacement of the walker as
depending on the properties of dwelling time distribution in each phase.
Depending on these distributions, normal diffusion, superdiffusion and
ballistic spreading may arise.
