Large deviations of bisexual branching process in random environment

We study large deviation probabilities for bisexual branching process in a random (i.i.d.) environment. Under several conditions on the mating function (which may depend on the environment) we introduce the associated random walk of the process. We also assume Cramer condition for the step of the walk and moment conditions on the number of descendants of one pair. Under Cramer condition for the steps of the walk and moment conditions on the number of descendants of a pair we find an exact asymptotics of probabilities ${\mathbf P}(\ln N_n \in [x,x+\Delta_n))$ as $n\to\infty$ for $x/n$ varying in some domain for all sequences $\Delta_n$, tending to zero sufficiently slowly. Similar results we obtain for bisexual branching process with immigration in a random environment.