Experimental and theoretical studies of the coupled-cavity diode-pumped Nd:YAG/Cr:YAG microchip lasers with intracavity Raman conversion of laser pulses in a Ba(NO3)2 crystal into two Stokes pulses have been made. Two lasers with a different cavity length have been investigated. The minimal pulse durations at the 2nd Stokes wavelength were ≈100 ps in the short-cavity laser at pulse energy of 5 μJ, and the pulse repetition rate reached 20–24 kHz. The laser and Stokes pulse dynamics, as well as the spatial intensity distribution of the laser and the 1st Stokes beams at the output mirror have been recorded. A model describing such coupled-cavity microchip Raman lasers has been developed. The numerically simulated laser and Stokes pulse dynamics, and the calculated pulse energy, duration, and repetition rate are in good agreement with the experimental data.