The author studies abstract conditions on the pair (dim N,dim P) under which the set of \(C^{\infty}\)-stable maps \(N\to P\) is not dense in \(C^{\infty}(N,P)\), and also conditions under which there are no \(C^{\infty}\)-stable maps in a given homotopy class of maps \(N\to P\). The paper contains some interesting results on differentiable maps and also discusses some well-known properties which are essential for the author’s work on mappings of finite codimension.