The following preprint is available: M. Grandis, Directed homotopy theory, II. Homotopy constructs, Dip. Mat. Univ. Genova, Preprint 446 (Dec 2001). (19 p.) ___ Abstract. Directed Algebraic Topology studies phenomena where privileged directions appear, derived from the analysis of concurrency, traffic networks, space-time models, etc. This is the sequel of a paper, 'Directed homotopy theory, I. The fundamental category', where we introduced directed spaces, their non reversible homotopies and their fundamental category. Here we study some basic constructs of homotopy, like homotopy pushouts and pullbacks, mapping cones and homotopy fibres, suspensions and loops, cofibre and fibre sequences. ___ Part I and II are available, in ps: ftp://www.dima.unige.it/Home/grandis/public/Dht1.ps ftp://www.dima.unige.it/Home/grandis/public/Dht2.ps ___ Marco Grandis Dipartimento di Matematica Universita' di Genova via Dodecaneso 35 16146 GENOVA, Italy e-mail: grandis@dima.unige.it tel: +39.010.353 6805 fax: +39.010.353 6752 http://www.dima.unige.it/~grandis/ ftp://www.dima.unige.it/Home/grandis/public/