Abstract: An agent is asked to traverse a graph. He is allowed to visit every vertex more than once, but he should report every vertex exactly once. This is an easy task when the agent has enough memory, or equally, can leave an unlimited number of mark bits on the vertices of the graph. Suppose this benefit is taken from the agent. If the agent has access to no other information about the graph, then his chances to succeed are zero for general graphs. Thus, we supply some additional information to the agent and see if this increases his chances. For example, suppose the agent can use only a constant number of mark bits and suppose the graph is a geometric graph---embedded into the plane (not necessarily planar embedded) and vertices are aware of their coordinates. Does this information increase agent's chances? The answer is positive. First local traversal algorithm developed was able to traverse geometric planar triangulations. Later the algorithm was extended to traverse vertices of an arrangement or a convex polytope. The research progressed to an algorithm that can traverse any geometric planar graph. In this talk, we extend the notion of planar graph to quasi-planar graph in which we allow many edges to cross each other. We describe an algorithm for traversal of any geometric quasi-planar graph that satisfies a simple condition. The worst case running time of our algorithm is O(|E|log|E|) which matches the running time of the traversal algorithm for planar graphs.