Abstract.We have selected seven medium-distant clusters of galaxies (z ∼ 0.1-0.3) for multi-wavelength observations with the goal of investigating their dynamical state. Following Paper I (Pierre et al. 1999) which reported the ASCA results about two of them, we present here the analysis of the ASCA observations of the other five clusters; RX J1023.8-2715 (A 3444), RX J1031.6-2607, RX J1050.5-0236 (A 1111), RX J1203.2-2131 (A 1451), and RX J1314.5-2517. Except for RX J1031.6, whose X-ray emission turned out to be dominated by an AGN, the ASCA spectra are well fitted by a one-temperature thin thermal plasma model. We compare the temperatureluminosity relation of our clusters with that of nearby ones (z < 0.1). Two clusters, RX J1050.5 and RX J1023.8, show larger luminosities than the bulk of clusters at similar temperatures, which suggests the presence of a cooling flow. The temperature vs. iron-abundance relationship of our sample is consistent with that of nearby clusters.