A two-dimensional projection tensor formalism for treating spacetimes with two commuting Killing vectors is presented and its use is illustrated by two examples---an alternative proof of a sufficient condition for such a spacetime to be orthogonally transitive and an application to the Rainich-Misner-Wheeler geometrization of the electromagnetic field to derive a result previously obtained by Michalski and Wainright. Finally, the admissible Petrov types are investigated and it is proved, in particular, that all vacuum fields with two commuting orthogonally transitive Killing vectors ${{\ensuremath{\xi}}_{0}}^{\ensuremath{\mu}}$ and ${{\ensuremath{\xi}}_{1}}^{\ensuremath{\mu}}$ satisfying $\mathrm{det}({\ensuremath{\xi}}_{a}^{\ensuremath{\mu}}{\ensuremath{\xi}}_{b\ensuremath{\mu}})\ensuremath{\ne}\mathrm{const}$, except the van Stockum metric (which is in general type II), are either type I or type D.