  In this paper we study a general class of hybrid mathematical models of
collective motions of cells under the influence of chemical stimuli. The models
are hybrid in the sense that cells are discrete entities given by ODE, while
the chemoattractant is considered as a continuous signal which solves a
diffusive equation. For this model we prove the mean-field limit in the
Wasserstein distance to a system given by the coupling of a Vlasov-type
equation with the chemoattractant equation. Our approach and results are not
based on empirical measures, but rather on marginals of large number of
individuals densities, and we show the limit with explicit bounds, by proving
also existence and uniqueness for the limit system. In the monokinetic case we
derive new pressureless nonlocal Euler-type model with chemotaxis.
