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Let A and B be unital C*-algebras, and let J ∈ A, L ∈B be Hermitian invertible elements. For every T ∈ A and S ∈ B, define Tj+ = J-1T*J and S+L = L-1S*L. Then in such a way we endow the C*-algebras A and B with indefinite structures. We characterize firstly the Jordan (J, L)-+-homomorphisms on C*-algebras. As applications, we further classify the bounded linear maps Φ: A →B preserving (J, L)-unitary elements. When A =B(H) andB =B(K), where H and K are infinite dimensional and complete indefinite inner product spaces on real orcomplex fields, we prove that indefinite-unitary preserving bounded linear surjectionsare of the form T → UVTV-1 (( )T ∈ B(H)) or T → UVT+V-1 (( )T ∈ B(H)),where U ∈ B(K) is indefinite unitary and, V: H → K is generalized indefinite unitary in the first form and generalized indefinite anti-unitary in the second one.Some results on indefinite orthogonality preserving additive maps are also given.