Biduals of tensor products in operator spaces

We study whether the operator space V** circle times(alpha) W** can be identified with a subspace of the bidual space (V circle times(alpha) W)**, for a given operator space tensor norm. We prove that this can be done if alpha is finitely generated and V and W are locally reflexive. If in addition the dual spaces are locally reflexive and the bidual spaces have the completely bounded approximation property, then the identification is through a complete is omorphism. When alpha is the projective, Haagerup or injective norm, the hypotheses can be weakened.