We present an ab initio method for computing multi-atom resonant photoemission (MARPE) in molecules and use this method to investigate the possibility of having a sizable MARPE effect. The MARPE cross section is obtained by making multi-center expansions of both the dipole matrix element - direct emission - and the hamiltonian matrix element between the resonant state and the autoionizing states -resonant emission. We show by sample calculations that the resonant contribution exhibits a strong distance dependence of the atoms participating in the MARPE process, and that it is energy dependent and element specific for the neighboring atoms. The ratio of resonant MARPE and direct photoionization cross sections is found to amount to less than one percent which probably makes the molecular MARPE effect difficult to apply in practice. (C) 2002 Elsevier Science B.V. All rights reserved.