  We consider various incommensurate (IC) order parameters for electrons on a
square lattice which reduce to $d_{x^2-y^2}$-density wave (DDW) order when the
ordering wavevector ${\bf Q}\to (\pi,\pi)$. We describe the associated charge
and current distributions and their experimental signatures. Such orders can
arise at the mean-field level in extended Hubbard models. We compare the phase
diagrams of these models with experiments in the underdoped cuprates, where (1)
DDW order is a possible explanation of the pseudogap, and (2) there are
experimental indications of incommensurability. We find various types of IC DDW
and discuss their possible relevance to the physics of the cuprates. Our main
finding is that IC DDW order is generally accompanied by superconducting order,
but the magnitude of the IC wavevector can be small. A comparison with the
analogous AF-ICSDW transition is given.
