The following preprint is available "Cubical homotopical algebra and cochain algebras" Marco Grandis. Abstract. Basic homotopical algebra is developed in a setting consisting of a cubical monad (*), i.e. a cylinder endofunctor I, equipped with connections g-, g+: I^2 -> I, and - possibly - with symmetries extending the reversion r: I -> I and the interchange s: I^2 -> I^2 of the standard topological case. Our study is mostly concerned with the Puppe sequence of a map f and its comparison with the sequence of iterated homotopy cokernels of f. As an application, the homotopy structure of cochain algebras is studied in the present frame, through the cubical co-monad of the path functor P and the left adjoint cylinder functor I. This paper is a sequel of (*) "Cubical monads and their symmetries", whose abstract appeared in "CATEGORIES", Mon, 4 Oct 1993. Regards, Marco Grandis Dipartimento di Matematica, Universita di Genova, Via L.B. Alberti 4, I - 16132 Genova, Italia e-mail: grandis@dima.unige.it