Summary: The effect of constraints on the initial value and acausal propagation problems in the Poincaré Gauge Theory is considered with the aid of linearized theory and Hamiltonian analysis. To linear order there are no difficulties, however non-linearities in any extra constraints can cause serious problems involving a change in the number and type of constraints as well as acausal propagation modes. Specific examples are given. Only very special parameter choices are expected to avoid these problems. A similar story is predicted for most other gauge theories of gravity. This type of analysis holds promise as a strong test for alternate gravity theories.