  In this paper, we study the Galton-Watson process in the random environment
for the particular case when the number of the offsprings in each generation
has the fractional linear generation function with random parameters. In this
case, the distribution of $N_t$, the number of particles at the moment time
$t=0,1,2,\cdots$ can be calculated explicitly. We present the classification of
such processes and limit theorems of two types: quenched type which is for the
fixed realization of the random environment and annealed type which includes
the averaging over the environment.
