We show that the Abelian Proca model, which is gauge noninvariant with
second class constraints can be converted into gauge theories with fi
rst class constraints. The method used, which we call gauge unfixing,
employs a projection operator defined in the original phase space. Thi
s operator can be constructed in more than one way and so we get more
than one gauge theory. Two such gauge theories are the Stuckelberg the
ory and the theory of Maxwell field interacting with an antisymmetric
tensor field. We also show that the application of the projection oper
ator does not affect the Lorentz invariance of this model.