  We study the dynamics of Kuznetsov-Ma solitons (KMS) in the framework of
vector nonlinear Schr\"odinger (Manakov) equations. Exact multi-parameter
family of solutions for such KMSs is derived. This family of solutions includes
the known results as well as the previously unknown solutions in the form of
the non-degenerate KMSs. We present the existence diagram of such KMSs that
follows from the exact solutions. These non-degenerate KMSs are formed by
nonlinear superposition of two fundamental KMSs that have the same propagation
period but different eigenvalues. We present the amplitude profiles of new
solutions, their exact physical spectra, their link to ordinary vector solitons
and offer easy ways of their excitation using numerical simulations.
