Pulse propagations in an amplifier in the case of the photodissociation iodine laser are investigated with the use of semiclassical treatments, especially when the input pulse fed into the amplifier has a width comparable to or shorter than the transverse relaxation time of the amplifier medium. In our semiclassical equations for pulse propagation in an iodine amplifier, the populations of all hyperfine levels [
2P
1/2(

),
2P
3/2(

)], the polarizations of optically allowed transitions (

), and the Doppler detuning effects were taken into consideration. Based on the numerical integrations of the semiclassical equations, the propagated pulse shape and the population distributions of the hyperfine levels are discussed. From our calculations, it has been made clear that bandwidth limitations of pulses in the range of pulsewidths of 0.1 ns and below can be avoided by making use of the nonlinear amplification that results from the coherent interaction between the propagated pulse field and the amplifier medium.