Subjects made fast, discrete elbow flexion movements while simultaneously producing rhythmical oscillations about initial and final visual targets embedded on a horizontal surface. Based on kinematic and electromyographic (EMG) analysis, we found that the discrete movement could start at any phase of the cyclical movement. The most likely onset time occurred when the first agonist burst started at the same moment as a rhythmical burst would have appeared. This resulted in a smooth conjugation between discrete and rhythmical movements. The initiation of the discrete movement was associated with the resetting of the phase of the rhythmical movements. Thus, the time characteristics of the two motor tasks were interdependent. A subset of trials with a uniform distribution of discrete movement onset phases could be selected in most subjects and was averaged to eliminate the cyclical component from the combined movement. Mean kinematic and EMG traces up until the peak velocity were practically identical to those of the discrete movement made alone. The averaging procedure was ineffective in eliminating the rhythmical component following the discrete movement because of the resetting of the phase of oscillation. Using the same procedure it has been shown that initiating the rhythmical movement at the same time as beginning the discrete movement did not affect the initial part of discrete movement. The whole discrete movement was not affected when subjects simultaneously terminated the ongoing rhythmical movements. Our findings are consistent with the hypothesis that although the rhythmical movement constrains the onset time of discrete movement, the latter, once initiated, proceeds independently of the ongoing rhythmical movement. We also subtracted the discrete component from the combined movement to see how the former affected the rhythmical movement. The residual pattern showed that the rhythmical movements rapidly attenuated when the discrete movement started and then apparently resumed after the peak velocity of the discrete movement. The results corroborate the hypothesis that the control signals underlying the two motor tasks cannot be applied simultaneously, since they may be associated with conflicting stability requirements. Instead, these control signals may be generated sequentially, but the resulting kinematic responses may outlast them and be superposed.