We consider gradation of pseudosmoothness of (in general, nonpolynomial) splines and find conditions under which the space of splines of maximal pseudosmoothness is unique on a given grid, possesses the embedding property on embedded grids, and satisfies the approximation relations. The proposed general scheme can be applied to splines generated by functions in spaces of integrable functions and in Sobolev spaces. The results are illustrated by some examples.