2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/216686We establish extension theorems for separately holomorphic mappings defined on sets of the form W\setminus M with values in a complex analytic space which possesses the Hartogs extension property. Here W is a 2-fold cross of arbitrary complex manifolds and M is a set of singularities which is locally pluripolar (resp. thin) in fibers.30 pages. A previous version is available at the ICTP preprints website (ref. IC2007073)Complex Variables32D15, 32D10text