From the very definition, it follows that every Jordan k-derivation of a gamma ring M is, in general, not a k-derivation of M. In this article, we establish its generalization by considering M as a 2-torsion free semiprime Γ N -ring (Nobusawa gamma ring). We also show that every Jordan k-derivation of a 2-torsion free completely semiprime Γ N -ring is a k-derivation of the same.