  We deal with the problem of description of nonsingular pairs of compatible
flat metrics for the general $N$-component case. We describe the scheme of the
integrating the nonlinear equations describing nonsingular pairs of compatible
flat metrics (or, in other words, nonsingular flat pencils of metrics). It is
based on the reducing this problem to a special reduction of the Lame equations
and the using the Zakharov method of differential reductions in the dressing
method (a version of the inverse scattering method).
