Making use of the orbital elements taken from Ephemerides of Minor Planets for 1977, shortest distances, inferior to 0.0004 AU, have been determined of the asteroid orbits pairs with mutual inclinations not exceeding $0^{\circ},500$. All the numbered minor planets have been examined, out of which 142, forming 77 pairs, have been found to conform to the two previous conditions. Minimum distances of the asteroid orbits have been found which until now were unknown. With some of the pairs these distances are extremely small and might be regarded as curiosities. 13 orbital pairs have been found with minimal distances less than 10000 km, 600 km being the smallest among them.