  For an odd prime p, we construct integral models over p for Shimura varieties
with parahoric level structure, attached to Shimura data (G,X) of abelian type,
such that G splits over a tamely ramified extension of Q_p. The local structure
of these integral models is related to certain "local models", which are
defined group theoretically. Under some additional assumptions, we show that
these integral models satisfy a conjecture of Kottwitz which gives an explicit
description for the trace of Frobenius action on their sheaf of nearby cycles.
