  We propose two nonlinear random walk models which are suitable for the
analysis of both chemotaxis and anomalous transport. We derive the balance
equations for the population density for the case when the transition rate for
a random walk depends on residence time, chemotactic substance and population
density. We introduce the anomalous chemotactic sensitivity and find anomalous
aggregation phenomenon. So we suggest a new explanation of the well-known
effect of chemotactic collapse. We develop a non-Markovian "velocity-jump"
model and obtain the superdiffusive behavior of bacteria with power law "run"
time.
