Neutron-multiwave-interference phenomena based on Ramsey’s resonance method of “separated oscillating fields” are studied. A neutron passes through N successive resonant coils [Formula Presented] which flip the neutron spin with a probability [Formula Presented] smaller than 1. These coils are separated by path lengths L over which a homogeneous field [Formula Presented] is present. Because the spin-flip probability [Formula Presented] is smaller than 1, the number of waves for a neutron is doubled after each flipper, so as to produce [Formula Presented] neutron waves at the end of the setup. The phase difference between any pair of waves is a multiple of a “phase quantum” determined by the line integral of the field difference [Formula Presented] over the length L. Highly regular patterns of the quantum-mechanical probability R in [Formula Presented] space appear due to pair interference between individual waves. Possible applications of this phenomenon, such as a direct measurement of n-particle correlation function, are pointed out.