Accumulated photon echoes have been used to investigate the mechanisms of optical dephasing in CaF2 crystals activated by Nd3+ ions. Tunable picosecond laser radiation, which permits the selective excitation of various Nd3+ optical centers in the 4I9/2→4G5/2, 2G7/2 transition, is used. The optical phase relaxation times measured at temperatures from 9 to 50 K permit determination of the homogeneous widths of the transitions between the low-lying 4I9/2 Stark level and three excited 4G5/2, 2G7/2 levels, and calculation of the constants of the inter-Stark relaxation transitions in the ground and excited multiplets for the rhombic N and M Nd3+ centers in CaF2 crystals. An analysis of the temperature dependence of the homogeneous linewidth of the transitions between low-lying Stark levels of the ground and excited states shows that the mechanism of optical dephasing in the crystals investigated is described well by direct relaxation processes with resonant inter-Stark absorption of one phonon in the ground and excited states. At T=9 K, the homogeneous linewidth Γh in CaF2 crystals is almost an order of magnitude smaller than Γh in disordered CaF2-YF3 crystals. This difference can be attributed to the significantly greater spectral phonon density of states in disordered crystals.