We present the results of a kinematical and morphological study of galaxies in the Hickson compact groups. The redshift survey of 457 galaxies has been completed. The great majority of the galaxies have velocities within about 1000 km/s(exp -1) of the median velocity of the group. The velocities of the groups range from 1380 to 41731 km/s(exp -1) with a median of 8889 km/s(exp -1), corresponding to a median distance of 89 h(exp -1)Mpc. With the addition of the radial velocity selection criterion, a relatively large sample of physically dense compact groups was defined. The nature of the velocity dispersion-morphology relation (Hickson, Kindl and Huchra 1989, hereafter HKH) is investigated. This is the tendency of groups with high velocity dispersions to contain fewer late type galaxies. We find that this strong correlation is not due to any sample selection effects. The morphology concordance in compact groups (HKH), which is the trend for galaxies in a group to have similar morphological types, can be fully explained by the velocity dispersion-morphology correlation. A significant correlation is found between crossing time and the fraction of gas-rich galaxies in the groups. Groups with short crossing times typically contain fewer late-type galaxies. This may be evidence that significant dynamical evolution has occurred in these groups.