  We show that the most general two--matrix model with bilinear coupling
underlies $c=1$ string theory. More precisely we prove that $W_{1+\infty}$
constraints, a subset of the correlation functions and the integrable hierarchy
characterizing such two--matrix model, correspond exactly to the $W_{1+\infty}$
constraints, to the discrete tachyon correlation functions and to the
integrable hierarchy of the $c=1$ string.
