We have recently succeeded to synthesize pure-phase of K2CuCl2SO4 and Na2CuCl2SO4. In addition, we succeeded to grow the large single crystals (~ 10×10×10 mm3). K2CuCl2SO4 is a good candidate compound for the S = 1/2 zigzag spin chain system. Moreover, our experimental results are indicating that K2CuCl2SO4 is only sample which can be investigate the spin nematic state by using muSR and inelastic neutron scattering method. On the other hand, the development of short-range correlations at around 10 K and the long-range ordering at 0.5 K was observed in Na2CuCl2SO4. Firstly, we should investigate the spin dynamics of K2CuCl2SO4 and Na2CuCl2SO4 in zero field (and weak LF). In this experiment, we expect to observe the characteristic spin dynamics of a vector chiral state in K2CuCl2SO4 and an unconventional spin dynamics between 0.5 K and 10 K in Na2CuCl2SO4.