  We show that with every classical system possessing first class constraints
that form a natural Lie algebra, we can associate a superalgebra that admits
the constraint Lie algebra as a subalgebra. An odd generator of this
superalgebra that commutes with the constraints is shown to be the BRST
operator whose form follows from a non linear coset representation of the
superalgebra. We further show the existence of the superalgebra for all
Yang-Mills theories and for 26-dimensional bosonic strings.
