We reformulate and extend "morphic cohomology" developed by the author and
H.B. Lawson so that, together with "Lawson homology", it satisfies the axio
ms of S. Bloch and A. Ogus for a "Poincare' duality theory with supports" o
n complex quasi-projective varieties. (C) 2000 Editions scientifiques et me
dicales Elsevier SAS.