  We have evaluated the amplitude for muon capture by a proton, mu + p --> n +
nu, to O(p^3) within the context of heavy baryon chiral perturbation theory
(HBChPT) using the new O(p^3) Lagrangian of Ecker and Mojzis (E&M). We obtain
expressions for the standard muon capture form factors and determine three of
the coefficients of the E&M Lagrangian, namely, b_7, b_{19}, and b_{23}. We
describe progress on the next step, a calculation of the radiative muon capture
process, mu + p --> n + nu + gamma.
