Today's mobile, desktop, and server processors are heterogeneous, consisting not only of CPUs but also GPUs and other accelerators. Such heterogeneous processors are starting to expose a shared memory interface across these devices.Given that each of these individual devices typically supports a distinct instruction set architecture and a distinct memory consistency model, it is not clear what the memory consistency model of the heterogeneous machine should be. In this paper, we answer this question by formalizing "compound"memory models: we present a compositional operational model describing the resulting model when devices with distinct consistency models are fused together. We instantiate our model with the compound x86TSO/PTX model-a CPU enforcing x86TSO and a GPU enforcing the PTX model. A key result is that the x86TSO/PTX compound model retains compiler mappings from the language-based (scoped) C memory model. This means that threads mapped to the x86TSO device can continue to use the already proven C-To-x86TSO compiler mapping, and the same for PTX.