A zigzag in a k-valent plane graph G is a circuit of edges, such that any two, but not three consecutive edges belong to the same face. A railroad in G is a circuit of evengonal faces, such that any face is adjacent to its neighbors on opposite edges. Boundary circuits of a railroad are two ”parallel” zigzags if k = 3, or, in a 4-valent graph, two such central circuits. We consider the zigzag and railroad structure of two-faced 3- and 4-valent plane graphs (generalizations of Platonic polyhedra) and their connections with other problems.