  We present a new approach to construction of recursion operators for
multidimensional integrable systems which have a Lax-type representation in
terms of a pair of commuting vector fields. It is illustrated by the examples
of the Manakov--Santini system which is a hyperbolic system in N dependent and
N + 4 independent variables, where N is an arbitrary natural number, the
six-dimensional generalization of the first heavenly equation, the modified
heavenly equation, and the dispersionless Hirota equation.
