  We present the study of weakly bound, neutron-rich nuclei using the nuclear
shell model employing the complex Berggren ensemble representing the bound
single-particle states, unbound Gamow states, and the non-resonant continuum.
In the proposed Gamow Shell Model, the Hamiltonian consists of a one-body
finite depth (Woods-Saxon) potential and a residual two-body interaction. We
discuss the basic ingredients of the Gamow Shell Model. The formalism is
illustrated by calculations involving {\it several} valence neutrons outside
the double-magic core: $^{6-10}$He and $^{18-22}$O.
