The general (non-spatial) stochastic epidemic is extended to allow infective individuals to move forward through a system of spatially connected locations · ··, L1, L2, · ·· (on the line) each containing susceptible individuals and the outcome of the epidemic in each of these locations is then considered. In the deterministic case, a (spatial) equilibrium solution and threshold behaviour are discussed. In the stochastic case, a (spatial) quasi-equilibrium behaviour (conditional on sufficient numbers of infectives present) is discussed; numerical results suggest some correspondence between this stochastic quasi-equilibrium and the deterministic equilibrium.