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We show how to reduce, under certain regularities conditions, aPoisson-Nijenhuis Lie algebroid to a symplectic-Nijenhuis Lie algebroid withnondegenerate Nijenhuis tensor. We generalize the work done by Magri and Morosifor the reduction of Poisson-Nijenhuis manifolds. The choice of the moregeneral framework of Lie algebroids is motivated by the geometrical study ofsome reduced bi-Hamiltonian systems. An explicit example of reduction of aPoisson-Nijenhuis Lie algebroid is also provided.

Reduction of Poisson-Nijenhuis Lie algebroids to symplectic-Nijenhuis Lie algebroids with nondegenerate Nijenhuis tensor