The particle and event horizons are widely known and studied concepts, but the study of their properties, in particular their evolution, have only been done so far considering a single state equation in a decelerating universe. This paper is the first of two where we study this problem from a general point of view. Specifically, this paper is devoted to the study of the evolution of these cosmological horizons in an accelerated universe with two state equations, cosmological constant and dust. We have obtained simple expressions in terms of their respective recession velocities that generalize the previous results for one state equation only. With the equations of state considered, it is proved that both velocities remain always positive.