We examine the lattice boundary formulation of chiral fermions with either an explicit Majorana mass or a Higgs-Majorana coupling introduced on one of the boundaries, We demonstrate that the low-lying spectrum of the models with an explicit Majorana mass of the order of an inverse lattice spacing is chiral at tree level, Within a mean-field approximation we show that the systems with a strong Higgs-Majorana coupling have a symmetric phase, in which a Majorana mass of the order of an inverse lattice spacing is generated without spontaneous breaking of the gauge symmetry. We argue, however, that the models within such a phase have a chiral spectrum only in terms of the fermions that are singlets under the gauge group. The application of such systems to non-perturbative formulations of supersymmetric and chiral gauge theories is briefly discussed. (C) 1997 Published by Elsevier Science B.V.