The following preprint is available: M. Grandis, Exactness and stability in homotopical algebra, Dip. Mat. Univ. Genova, Preprint 419 (2000) Abstract. Exact sequences are a well known notion in homological algebra. We investigate here the more vague properties of 'homotopical exactness', appearing for instance in the fibre or cofibre sequence of a map. Such notions of exactness can be given for very general 'categories with homotopies' having homotopy kernels and cokernels, but become more interesting under suitable 'stability' hypotheses, satisfied - in particular - by chain complexes. It is then possible to measure the default of homotopical exactness of a sequence by the homotopy type of a certain object, a sort of 'homotopical homology'. Available as ps-file at: ftp://pitagora.dima.unige.it/WWW/FTP/GRANDIS/Exa.Aug00.ps (255 K) or via home page: http://www.dima.unige.it/STAFF/GRANDIS/ With best regards, 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