  We consider the principal subspaces of certain level $k\geqslant 1$
integrable highest weight modules and generalized Verma modules for the
untwisted affine Lie algebras in types $D$, $E$ and $F$. Generalizing the
approach of G. Georgiev we construct their quasi-particle bases. We use the
bases to derive presentations of the principal subspaces, calculate their
character formulae and find some new combinatorial identities.
