The basic properties of the ground states in the four-body muon molecu
les pp mu mu, pd mu mu, pt mu mu, dd mu mu, dt mu mu, and tt mu mu are
calculated. It is found that the nuclear reaction rates (R(f)) in suc
h four-body molecules are significantly larger than for the correspond
ing three-body ions with the same nuclei: pp mu, pd mu, pt mu, dd mu,
dt mu, and tt mu. In particular, for the dt mu mu system R(f)(dt) appr
oximate to 3 x 10(13)-6x10(13) sec(-1), which is approximate to 40 tim
es greater than the respective R(dt)(dt mu) value.