We present force plate data on vertical free moments (force couples in the horizontal plane between the foot and the ground) and on transverse force during unloaded walking in different modes and at different speeds (including running) by adults of both sexes and by children, and examine loaded walking by adult males and one boy. Free moments in slow and normal-speed walking are characterised by a lateral peak in the accelerative phase of stance, but the peak during running, and in some cases of fast walking, occurs in the deceleration phase. Free moments are strongly affected by arm fixation in males, but less so in females. The pattern, but not the scale, of free moments is affected by loading position and side, but load magnitude has little effect if the loaded weight is treated as part of the body. Transverse force is more variable than sagittal force. In males, the transverse force curve shows a marked trough at mid-stance, whereas in females this trough is rarely seen. The transverse force of males also differs from that of females in response to arm fixation, showing a local medial inflection at three-quarters of the stance phase that is not present in females. Adults differ from children younger than 9 years in the presence of a very short, medially directed peak following heel-strike. Analysis of the effects of arm fixation and the timing of forces suggests strongly that arm-swing and free moments tend to reinforce each other in balancing trunk torques induced by the lower limbs. Both are of reduced importance in slow walking.