Measuring the rate of muon capture in hydrogen provides one of the most direct ways to study the axial current of the nucleon. The MuCap experiment uses a negative muon beam stopped in a time projection chamber operated with ultra-pure hydrogen gas. Surrounded by a decay electron detector, the lifetime of muons in hydrogen can be measured to determine the singlet capture rate Lambda_s to a final precision of 1%. The capture rate determines the nucleon's pseudoscalar form factor g_p. A first result, g_p = 7.3 +- 1.1, has been published and the final analysis of the full statistics will reduce the error by a factor of up to 3. Muon capture on the deuteron probes the weak axial current in the two-nucleon system. Within the framework of effective field theories the calculation of such two-nucleon processes involving the axial current requires the knowledge of one additional low energy constant which can be extracted from the doublet capture rate Lambda_d. The same constant then allows to model-independently calculate related processes such as solar pp-fusion or neutrino-deuteron scattering. The MuSun experiment will deduce Lambda_d to better than 1.5%. The experiment uses the MuCap detection setup with a new time projection chamber operated with deuterium at 30K and several hardware upgrades. The system is currently fully commissioned and the main physics data taking will start in 2011.

Invited talk at Physics of fundamental Symmetries & Interactions (PSI2010), October 11-14, 2010, Paul Scherrer Institut, Switzerland. To be published in Physics Procedia