  We consider existence and stability of an almost periodic solution of the
quasilinear system of differential equations with piecewise constant argument
of generalized type. The associated linear homogeneous system satisfies
exponential dichotomy. The deviations of the argument are not restricted by any
sign assumption when existence is considered. The problem of positive (almost
periodic) solutions of the logistic equation is discussed as an example.
  A new technique of investigation of equations with piecewise argument, based
on integral representation, is developed.
