  We construct combinatorial bases of principal subspaces of standard modules
of level $k \geq 1$ with highest weight $k\Lambda_0$ for the twisted affine Lie
algebras of type $A_{2l-1}^{(2)}$, $D_l^{(2)}$, $E_6^{(2)}$ and $D_4^{(3)}$.
Using these bases we directly calculate characters of principal subspaces.
