A real-valued function on R^n is k-regulous, where k is a nonnegative
integer, if it is of class C^k and can be represented as a quotient of two
polynomial functions on R^n. Several interesting results involving such
functions have been obtained recently. Some of them (Nullstellensatz, Cartan's
theorems A and B, etc.) can be carried over to a new setting of Nash regulous
functions, introduced in this paper. Here a function on a Nash manifold X is
called Nash k-regulous if it is of class C^k and can be represented as a
quotient of two Nash functions on X
