  Orbital stability property for weakly coupled nonlinear Schr\"odinger
equations is investigated. Different families of orbitally stable standing
waves solutions will be found, generated by different classes of solutions of
the associated elliptic problem. In particular, orbitally stable standing waves
can be generated by least action solutions, but also by solutions with one
trivial component whether or not they are ground states. Moreover, standing
waves with components propagating with the same frequencies are orbitally
stable if generated by vector solutions of a suitable single Schr\"odinger
weakly coupled system, even if they are not ground states.
