The ability of biological cells to migrate towards
chemoattractants is essential for many (patho-)physiological processes
such as wound healing or tumor metastasis. Chemotaxis is transduced by
complex molecular signaling cascades coupling to the intrinsic cell
migration machinery. The overall effect can be assessed with time-lapse
video microscopy of single migrating cells. We analyze experimental
paths of cells within the concept of stochastic processes to gain
further insight into the biological activities. The cell is regarded as
an object driven by internally correlated stochastic forces and
external fields generated by chemoattractants. The analysis is applied
to neutrophiles and tumor like transformed MDCK-F cells. Even in a
homogeneous environment, both cell types show a variety of anomalous
properties as superdiffusion that can be characterized by strong
temporal correlations and within the framework of a fractional
Klein-Kramers equation. The anomalous behavior is even conserved under
the influence of chemoattractants which might be useful for an
appropriate response to chemoattractants.