In ACrF5 (A = Cs, Rb, K), Cr(IV) ions are coordinated by six fluoride ligands where the resulting CrF6 octahedra share cis vertexes to form infinite chains of ([CrIVF5]−)n. The geometry of the latter in Cs compound differs from that in K and Rb compounds. The results of investigations of the magnetic behaviour of these compounds have shown that an antiferromagnetic superexchange interaction is present within the chains with JCs = −10.2 cm−1, JRb = −13.3 cm−1, and JK = −13.1 cm−1. Additional ferromagnetic-like long-range ordering has been observed in KCrF5 and RbCrF5 below 6 K which can be explained, in a correlation with their crystal structures, as canted antiferromagnetism.