A nitrogen laser pumped relaxation-oscillation-dye-laser with subnanosecond pulses is described in this paper. The formation processes of its relaxation oscillations and subnanosecond pulses have been observed. Approximate analytic solutions for the rate equations have been obtained in different stages of the initial transient process of the dye laser. The pulse width has been estimated by substituting the parameters and experimental values into the solutions, and the result agrees with that of the experimental values into the solutions^ and tho result agrees with that of the experiments within ail order of magnitude.