  We study semistable symmetric spectra based on quite general monoidal model
categories, including motivic examples. In particular, we establish a
generalization of Schwede's list of equivalent characterizations of
semistability in the case of motivic symmetric spectra. We also show that the
motivic Eilenberg-MacLane spectrum and the algebraic cobordism spectrum are
semistable. Finally, we show that semistability is preserved under localization
if some reasonable conditions - which often hold in practice - are satisfied.
