A generalized eutectic theory, which defaults to the prior theories by Jackson-Hunt and Trivedi et al. under their boundary conditions, has been developed to consider phase relations, solidification temperature and interface velocity over the entire parametric range, and for both lamellar and rod eutectic morphologies. The analytical solution reveals that lambda(2)V and lambda Delta T, though varying with the Peclet number, are virtually constant at very low Peclet number (crystal growth conditions). These constant values, however, map vary with the phase reaction and the degree of undercooling.