  We give the strong asymptotic of Cauchy biorthogonal polynomials under the
assumption that the defining measures are supported on non intersecting
intervals of the real line and satisfy Szeg\H{o}'s condition. The biorthogonal
polynomials are connected with certain mixed type Hermite-Pad\'e polynomials,
which verify full orthogonality relations with respect to some varying
measures. Thus, the strong asymptotic of orthogonal polynomials with respect to
varying measures plays a key role in the study.
