  Using exact numerical diagonalization and the conformal field theory
approach, we study the effect of magnetic frustrations due to diagonal exchange
bonds in a system of two coupled mixed-spin $(1,{1/2})$ Heisenberg chains. It
is established that relatively moderate frustrations are able to destroy the
ferrimagnetic state and to stabilize the critical spin-liquid phase typical for
half-integer-spin antiferromagnetic Heisenberg chains. Both phases are
separated by a narrow but finite region occupied by a critical
partially-polarized ferromagnetic phase.
