  We consider a specific class of manifolds with singularities, namely,
stratified manifolds, and describe a class of pseudodifferential operators
(PsiDO) related to differential operators with degeneration of first-order with
respect to the distance to the strata on such manifolds. (For manifolds with
isolated singularities, this is a Fuchs type degeneration.) We restrict
ourselves to the case of zero-order operators in L^2 spaces. The definition of
PsiDO adopted in our approach uses induction over the number of strata in the
manifold. The induction process naturally involves PsiDO with parameters.
