Let (L,[p]) be a finite dimensional restricted Lie algebra over a field K of positive characteristic p. A Jordan–Chevalley–Seligman decomposition of x∈L is a unique expression of x as a sum of commuting semisimple and nilpotent elements in L. It is well-known that each x∈L has such a decomposition when K is perfect. When K is non-perfect, the present paper gives several criteria for the existence of a Jordan–Chevalley–Seligman decomposition for a given x∈L as well as for determining when an element in the restricted subalgebra generated by x is semisimple or nilpotent.