Triangle spin tubes have attracted much attention because they possess characteristics of one-dimensional Heisenberg antiferromagnets along the tubes and geometrical spin frustration in each triangle plane. We performed X-ray diffraction, magnetic susceptibility, and heat capacity experiments on triangle spin tubes composed of CsCrF4 and alpha-KCrF4. In CsCrF4, no anomaly indicating an antiferromagnetic long-range order appeared, and a spin-liquid state was realized. In contrast, in alpha-KCrF4, antiferromagnetic long-range order occurred at T-N2 = 4.0(1) K and another phase transition occurred at T-N1 = 2.5(1) K. Such successive phase transitions may suggest a simultaneous change of the spin and crystal structures owing to a magnetoelectric effect.