In this chapter we continue to consider differential equations with piecewise constant argument of generalized type. New elaborated results which concern, first of all, linear systems of differential equations are under discussion. An exceptional attention to the exponential dichotomy is given at the first time in literature in the paper Akhmet (Discontinuity Nonlinearity Complexity 1:337-352, 2012). This time we present integral representation formulas. Moreover, bounded, almost periodic, and periodic solutions and their stability are considered. The notations, formulations of theorems have been made in such a way that further construction of the theory of differential equations will follow the structure of that for ordinary differential equations. All the results are illustrated with examples.