Polymethineimines (PMI's) and poly(2,3-diazabutadienes)(PBD's) are isoelectronic with polyacetylenes (PA's), but they do not possess the electron-hole or the spatial symmetries of PA. While PMI has been synthesized, PDB still remains to be prepared in the laboratory. In this paper, we have calculated the properties of some low-lying electronic states of PMI and PDB polymers, employing a Pariser-Parr-Pople model Hamiltonian. The nitrogen-atom parameters used in the model are obtained after extensively testing them in simple nitrogen-containing molecules. The electronic states in small polymers are obtained by exactly solving the finite model Hamiltonians employing a valence-bond procedure. The energy levels and other properties of the infinite system are then obtained from extrapolations. Our studies show that the optical gap in a single strand of PMI is2.6\pm 0.2 eV, which is very close to the single-strand PA value of 2.8\pm 0.2 eV. The gap in PDB is 3.8\pm 0.4 eV and, unlike the case for PA systems, there are no "in-gap" states in PMI or PDB. The transition dipoles to these states from the ground state as well as dipole moments in the ground state point to a nonlocal nature of the ground and excited states