  The muon capture reactions 2H(\mu^-,\nu_\mu)nn and 3He(\mu^-,\nu_\mu)3H are
studied with conventional or chiral realistic potentials and consistent weak
currents. The initial and final A=2 and 3 nuclear wave functions are obtained
from the Argonne v18 or chiral N3LO two-nucleon potential, in combination with,
respectively, the Urbana IX or chiral N2LO three-nucleon potential in the case
of A=3. The weak current consists of polar- and axial-vector components. The
former are related to the isovector piece of the electromagnetic current via
the conserved-vector-current hypothesis. These and the axial currents are
derived either in a meson-exchange or in a chiral effective field theory
(chiEFT) framework. There is one parameter (either the N-to-\Delta axial
coupling constant in the meson-exchange model, or the strength of a contact
term in the chiEFT model) which is fixed by reproducing the Gamow-Teller matrix
element in tritium beta-decay. The model dependence relative to the adopted
interactions and currents (and cutoff sensitivity in the chiEFT currents) is
weak, resulting in total rates of 392.0 +/- 2.3 Hz for A=2, and 1484 +/- 13 Hz
for A=3, where the spread accounts for this model dependence.
