The theoretical study of strongly bound doubly excited electronic states, discussed by the authors for a series of homonuclear diatomic molecules, is extended to the case of heteronuclear diatomics. Using BeC as a prototype, it is shown that the significant bond shortening and strengthening shown in the isoelectronic B2 also persists in BeC, in spite of the much greater configuration mixing in BeC due to the lower symmetry. In particular, excitations of the form σ→π cause a predictable increase in (local) bond strength. Potential curves and spectroscopic constants are given for the low-lying states correlating up to the sixth dissociation channel. Compared to the ground state X 3Σ- with R e=3.20 bohr and ωe=905 cm-1, the doubly excited state 3 1Σ+ has a local minimum at R e=2.87 bohr where ωe=1294 cm-1, a significant bond strengthening comparable to the homonuclear diatomics. The contribution to the total (CI) wave function for each state is analyzed in terms of the dominant contributions from the important configurations. SCF potential curves for the pure configurations and MO contour maps are used to understand the relationship with the homonuclear case. Vertical transition moments for the most important transitions are given to help in identification of the (as yet unobserved) electronic absorption spectrum.