Parkinson's disease (PD) is a neurodegenerative disorder characterized by a variety of motor signs affecting gait, postural stability, and tremor. These symptoms can be improved when electrodes are implanted in deep brain structures and electrical stimulation is delivered chronically at high frequency (>100 Hz). Deep brain stimulation (DBS) onset or cessation affects PD signs with different latencies, and the long-term improvements of symptoms affecting the body axis and those affecting the limbs vary in duration. Interestingly, these effects have not been systematically analyzed and modeled. We compare these timing phenomena in relation to one axial (i.e., locomotion) and one distal (i.e., tremor) signs. We suggest that during DBS, these symptoms are improved by different network mechanisms operating at multiple time scales. Locomotion improvement may involve a delayed plastic reorganization, which takes hours to develop, whereas rest tremor is probably alleviated by an almost instantaneous desynchronization of neural activity in subcortical structures. Even if all PD patients develop both distal and axial symptoms sooner or later, current computational models of locomotion and rest tremor are separate. Furthermore, a few computational models of locomotion focus on PD and none exploring the effect of DBS was found in the literature. We, therefore, discuss a model of a neuronal network during DBS, general enough to explore the subcircuits controlling locomotion and rest tremor simultaneously. This model accounts for synchronization and plasticity, two mechanisms that are believed to underlie the two types of symptoms analyzed. We suggest that a hysteretic effect caused by DBS-induced plasticity and synchronization modulation contributes to the different therapeutic latencies observed. Such a comprehensive, generic computational model of DBS effects, incorporating these timing phenomena, should assist in developing a more efficient, faster, durable treatment of distal and axial signs in PD.