The stability of two-parameter families of walking vector solitons of coupled nonlinear Schrödinger equations in investigated. It is shown that all known, lowest-order soliton types, namely, slow, fast, vector in phase, and vector out of phase are dynamically stable in certain regions of the parameter space. The condition of linear marginal stability of the solitons is not necessarily given by an explicit geometric criterion, because soliton instability mediated by the existence of complex eigenvalues of the corresponding Lyapunov operator is found to occur also.

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