  We present a new class of macroscopic models for pedestrian flows. Each
individual is assumed to move towards a fixed target, deviating from the best
path according to the instantaneous crowd distribution. The resulting equation
is a conservation law with a nonlocal flux. Each equation in this class
generates a Lipschitz semigroup of solutions and is stable with respect to the
functions and parameters defining it. Moreover, key qualitative properties such
as the boundedness of the crowd density are proved. Specific models are
presented and their qualitative properties are shown through numerical
integrations.
