Modern computer graphics systems are able to render sophisticated 3D scenes consisting of millions of polygons. For most camera positions only a small collection of these polygons is visible. We address the problem of occlusion culling, i.e., determine hidden primitives. Aila, Miettinen, and Nordlund suggested to implement a FIFO buffer on graphics cards which is able to delay the polygons before drawing them [2]. When one of the polygons within the buffer is occluded or masked by another polygon arriving later from the application, the rendering engine can drop the occluded one without rendering, saving important rendering time. We introduce a theoretical online model to analyse these problems in theory using competitive analysis. For different cost measures we invent the first competitive algorithms for online occlusion culling. Our implementation shows that these algorithms outperform the FIFO strategy for real 3D scenes as well.