50 50 06 v 1 3 1 M ay 1 99 5 Conditional Lie - Bäcklund symmetry and reduction of evolution equations .

We suggest a generalization of the notion of invariance of a given partial differential equation with respect to Lie-Bäcklund vector field. Such generalization proves to be effective and enables us to construct principally new Ansätze reducing evolution-type equations to several ordinary differential equations. In the framework of the said generalization we obtain principally new reductions of a number of nonlinear heat conductivity equations u t = u xx + F (u, u x) with poor Lie symmetry and obtain their exact solutions. It is shown that these solutions can not be constructed by means of the symmetry reduction procedure.