We study perpetuality in the calculus of explicit substitutions λx. A reduction is called perpetual if it preserves the possibility of infinite reduction sequences. We then take a look at applications of this study: an inductive characterization of the λx-strongly normalizing terms, two perpetual reduction strategies for λx and finally a proof of strong normalization of a polymorphic lambda calculus with explicit substitutions Fes. To complete the study of Fes, the property of subject reduction is shown to hold by extending type assignments of the typing rules to allow non-pure types (types with possible occurrences of the type substitution operator).