By extending the underlying data structure by new elements, we also extend the intput/output relation generated by a program i.e., no existing run is killed, and no new one lying entirely in the old structure is created. We investigate this stability property for the weak second order semantics derived from nonstandard time models. It turns out that the light face, i.e., parameterless collection principle always induces stable semantics, but the bold face one may be unstable. We give an example where (...) an elementary extension kills a bold face run showing also that the light face semantics is strictly weaker than the bold face one. (shrink)