This paper is devoted to entire rational mapping in real algebraic geometry. Several results are proved, particularly an extension of a result of Bochnak and Kucharz stating that for \(X\) being any \(k\)-dimensional non-singular real algebraic set any entire rational map from \(X\) \(S^{2n-k}\) to \(S^{2n}\) is null homotopic. Here \(S^{2n}\) (the standard sphere) is replaced by any non-singular real algebraically variety homeomorphic to \(S^{2n}\). The methods of proof are rather elementary.