Direct coupling of computer models is often difficult for computational and logistical reasons. We propose coupling computer models by linking independently developed Gaussian process emulators (GaSPs) of these models. Linked emulators are developed that are closed form, namely normally distributed with closed form predictive mean and variance functions. These are compared with a more direct emulation strategy, namely running the coupled computer models and directly emulating the system; perhaps surprisingly, this direct emulator was inferior in all illustrations. Pedagogical examples are given as well as an application to coupling of real computer models.