<p>The present paper is concerned with the spatial dynamics of a nonlocal dispersal susceptible–infected–removed epidemic model with recruitment and standard incidence in general time heterogeneous (including periodic, almost periodic and uniquely ergodic) media. More specifically, we establish upper and lower estimates of spreading speed, and then provide some sufficient conditions for the existence and nonexistence of generalized transition waves of nonlocal dispersal epidemic model with general time dependence. In particular, our results are sharp in some special situations. We need to point out that, to overcome the difficulties brought by general time heterogeneous media and lack of comparison principle and compactness in the nonlocal dispersal non-cooperative system, we give some important priori estimates of the solutions to prove the existence of spreading speed and generalized transition waves by using lower and upper solution method and limit discussion.</p>