Time delays produced by dispersal are shown to stabilize Lotka-Volterra predator-prey models. The models are formulated as integrodifferential equations that describe local predator-prey dynamics and either intrapatch or interpatch dispersal. Dispersing individuals may (or may not) differ in the duration of their trips; these differences are captured via a distributed delay in the models. Our results include those of previous studies as special cases and show that the stabilizing effect continues to operate when the dispersal process is modeled more realistically.