I would like to make a question about the way dynare computes and decides for the reported steady state values. I have a model, that I know has multiple steady states (all with real roots and eigenvalues) but only one is stable. So I played in dynare with initial values close to the unstable ones, but it reports the ones that indeed produce the stable steady state. So I am wondering whether this always the case. Is dynare reporting only the stable steady state even if other SS might exist ?

No. Given the starting values you provide, Dynare uses a numerical solver to find the solution to the static model equations. Maybe you just provided good starting values close to the stable steady state.

Since I knew all the steady state values, i experiment by giving starting values close to the unstable ones on purpose (from below and from above) but i was always getting the steady steady values for the stable one. And the distance from the unstable to stable were reasonable high. for example x=0.17 in one case and 2.24 in the other.

That is why i was wondering about dynare. I am asking this, since I am working with OLG models and the multiplicity of the Steady States are usually the rule in a class of models, so it is crucial to me to know whether dynare was able to do this or was just by accident.

As far as I know, there is nothing guaranteeing which steady state will be selected. I am also not aware of any theoretical reason why a Newton solver should always converge to one particular steady state.