Given two hyperkaehler manifolds X and Y and a quaternionic instanton on the pro duct XxY, one can define a generalized Fourier-Mukai transform, which maps quate rnionic instantons on X to quaternionic instantons on Y. This construction encom passes the cases of the Nahm-Mukai transform on two dimensional complex tori and of the Fourier-Mukai transform on K3 surfaces.