Process calculi based in logic, such as $\pi $DILL and CP, provide a foundation for deadlock-free concurrent programming, but exclude non-determinism and races. HCP is a reformulation of CP which addresses a fundamental shortcoming: the fundamental operator for parallel composition from the $\pi $-calculus does not correspond to any rule of linear logic, and therefore not to any term construct in CP. We introduce HCP${-} _{\text {ND}}$, which extends HCP with a novel account of non-determinism. Our approach draws on bounded linear logic to provide a strongly-typed account of standard process calculus expressions of non-determinism. We show that our extension is expressive enough to capture many uses of non-determinism in untyped calculi, such as non-deterministic choice, while preserving HCP ’s meta-theoretic properties, including deadlock freedom.