  We construct a family of integrable hydrodynamic type systems with three
independent and n>1 dependent variables in terms of solutions of linear system
of PDEs with rational coefficients. We choose the existence of a
pseudopotential as a criterion of integrability. In the case n=2 this family is
a general solution of the classification problem for such systems. We give also
an elliptic analog of this family in the case n>2.
