In this dissertation we consider a model of a random walk, (Zn}, on R(1) where the distribution of (Zn} is dependent on a stochastic process (Yn} and is given by gy(z) where Yn-1 = y . Conditions on the environmental process (Yn} are given for which transience or recurrence of the random walk (Zn} can be detennined. The probability of n absorption and mean time problems are solved when (Yn} is a finite Markov chain and (Zn} is a classical random walk on the integer lattice
