A theoretical description of the "fast" (<50 ps) intersystem crossing (ISC) processes occurring during the photodissociation of HCo(CO)(4) is presented. The radiationless transitions are simulated by wave packet propagations on spin-orbit coupled two-dimensional potential energy surfaces (CASSCF/CCI) calculated along two reaction coordinates (q(a)=[Co-H] and q(b)=[Co-COax]). A mechanism of deactivation of the singlet excited state of HCo(CO)(4) initially populated on UV excitation has been proposed. This mechanism differs slightly from the one deduced from a one-dimensional simulation performed separately, either along the Co-H bond or along the Co-COax bond : (i) in a very short time scale (<20 fs) 35% of the system dissociates toward the primary products H+Co(CO)(4) ((1)E), whereas the (1)E-->(3)A(1) and (1)E-->(3)E intersystem crossings occur within 50 ps; (ii) as soon as the lowest triplet states are populated, the system dissociates either to H+Co(CO)(4) ((3)A(1)) or to H+Co(CO)(4) ((3)E) on the corresponding potential energy surfaces; (iii) the indirect photodissociation mechanism through ISC may be described as a succession of elementary transitions followed by the homolysis of the metal-hydrogen bond.