  We study bifurcations and spectral stability of solitary waves in coupled
nonlinear Schr\"odinger equations (CNLS) on the line. We assume that the
coupled equations possess a solution of which one component is identically
zero, and call it a $\textit{fundamental solitary wave}$. By using a result of
one of the authors and his collaborator, the bifurcations of the fundamental
solitary wave are detected. We utilize the Hamiltonian-Krein index theory and
Evans function technique to determine the spectral or orbital stability of the
bifurcated solitary waves as well as as that of the fundamental one under some
nondegenerate conditions which are easy to verify, compared with those of the
previous results. We apply our theory to CNLS with a cubic nonlinearity and
give numerical evidences for the theoretical results.
