Let H be a real Hilbert space and let F : H → H be a boundedly Lipschitzian and strongly monotone operator. We design three hybrid steepest descent algorithms for solving variational inequality V I ( C , F ) of finding a point x ∗ ∈ C such that 〈 F x ∗ , x − x ∗ 〉 ≥ 0 , for all x ∈ C , where C is the set of fixed points of a strict pseudocontraction, or the set of common fixed points of finite strict pseudocontractions. Strong convergence of the algorithms is proved.