  Bisexual Galton-Watson processes are discrete Markov chains where
reproduction events are due to mating of males and females. Owing to this
interaction, the standard branching property of Galton-Watson processes is
lost. We prove tightness for conveniently rescaled bisexual Galton-Watson
processes, based on recent techniques developed by Bansaye, Caballero and
M{\'e}l{\'e}ard. We also identify the possible limits of these rescaled
processes as solutions of a stochastic system, coupling two equations through
singular coefficients in Poisson terms added to square roots as coefficients of
Brownian motions. Under some additional integrability assumptions, pathwise
uniqueness of this limiting system of stochastic differential equations and
convergence of the rescaled processes are obtained. Two examples corresponding
to mutual fidelity are considered.
