  We propose the superconnection formalism to construct the off-shell
BRST-VSUSY superalgebra for D=4 BF theories. The method is based on the natural
introduction of physical fields as well as auxiliary fields via
superconnections and their associated supercurvatures defined on a superspace.
We also give a prescription to build the off-shell BRST-VSUSY exact quantum
action.
