The results of numerical modeling of nonstationary forward SRS of femt
osecond pulses in molecular dispersive gases are presented. The calcul
ations are carried out in one-dimensional two-wave approximation takin
g into account self- and cross-action of the pulses. For the first tim
e the dynamics of a Stokes pulse build-up and the transformation of it
s spectrum and temporal shape during amplification are traced up to th
e saturation regime in CH4, NH3, H-2, and SF6. The fundamental role of
group velocity mismatch, which determines the velocity of a Stokes pu
lse with respect to a pump pulse is revealed. It is shown that there e
xists a range of parameters where pulse compression takes place under
optimum amplification with drastic sharpening of the leading edge of t
he pulse. The parameters of SRS converter based on an oscillator and a
two-stage amplifier with beam summation at She second stage are calcu
lated. The pumping high-power femtosecond excimer system produces two
beams with an energy of 1 J each at the wavelength of 308 nm and pulse
duration of 300 fs. The converter provides conversion efficiency up t
o 60%, threefold compression of the pulse, prepulse suppression, and s
harpening of the leading edge.