  New method for construction of gauge-invariant deformed theory from an
initial gauge theory proposed in our previous papers [1], [2] for closed/open
gauge algebras is extended to the case of reducible gauge algebras. The
deformation procedure is explicitly described with the help of generating
functions of anticanonical transformations depending on fields of the initial
gauge action only. The deformed gauge-invariant action and the deformed gauge
generators are described with the help of the generating functions in a closed
and simple form. As an example of reducible gauge systems we consider the free
fermionic p-form fields or, in another words, the antisymmetric tensor-spinor
fields. It is proved that gauge-invariant deformation of fermionic p-form
fields leads always to non-local deformed theory which does not contain a
closed local sector. In its turn the model based on two fermionic 2-form fields
and a real massive scalar field admits local interactions between these fields
in local sector of the deformed action.
