Neutron magnetic scattering of intercalation compounds FexTiS2 has been measured systematically as a function of Fe concentration x In the x = 0.15 and 1/4 samples, so-called small-angle scattering was observed associated with a spin-glass transition. In the x = 1/2 sample, clear magnetic Bragg reflections were observed. The position of the magnetic peak with the smallest Q number was not commensurate with the nuclear lattice-unit. The magnetic structure of Fe1/2TiS2 was found not to be a simple ferromagnetic structure as was ever suggested but a long-period magnetic structure. In the x = 1/3 sample, broad magnetic diffuse peak whose Q number was also not commensurate with the nuclear lattice-unit was observed. The origin of the magnetism of Fe1/3TiS2, what is called a duster-glass, seems the short-range ordered magnetic-clusters with a long-period magnetic structure.