  Recent studies have indicated that cosmic ray acceleration by a first-order
Fermi process in magnetic reconnection current sheets can be efficient enough
in the surrounds of compact sources. In this work, we discuss this acceleration
mechanism operating in the core region of galactic black hole binaries (or
microquasars) and show the conditions under which this can be more efficient
than shock acceleration. In addition, we compare the corresponding acceleration
rate with the relevant radiative loss rates obtaining the possible energy
cut-off of the accelerated particles and also compute the expected spectral
energy distribution (SED) for two sources of this class, namely Cygnus X-1 and
Cygnus X-3, considering both leptonic and hadronic processes. The derived SEDs
are comparable to the observed ones in the low and high energy ranges. Our
results suggest that hadronic non-thermal emission due to photo-meson
production may produce the very high energy gamma-rays in these microquasars.
