We propose a real-time, direct monocular SLAM method for omnidirectional or wide field-of-view fisheye cameras. Both tracking (direct image alignment) and mapping (pixel-wise distance filtering) are directly formulated for the unified omnidirectional model, which can model central imaging devices with a field of view above 180°. This is in contrast to existing direct mono-SLAM approaches like DTAM or LSD-SLAM, which operate on rectified images, in practice limiting the field of view to around 130° diagonally. Not only does this allows to observe - and reconstruct - a larger portion of the surrounding environment, but it also makes the system more robust to degenerate (rotation-only) movement. The two main contribution are (1) the formulation of direct image alignment for the unified omnidirectional model, and (2) a fast yet accurate approach to incremental stereo directly on distorted images. We evaluated our framework on real-world sequences taken with a 185° fisheye lens, and compare it to a rectified and a piecewise rectified approach.