This study investigates a task in which discrete and rhythmic movements are combined in a single-joint elbow rotation. Previous studies reported a tendency for the EMG burst associated with the discrete movement to occur around the expected burst associated with the rhythmic movement (e.g., [Exp. Brain Res. 99 (1994) 325; J. Neurol. Neurosurg. Psychiatry 40 (1977) 1129; Hum. Mov. Sci. 19 (2000) 627]). We document this interaction between discrete and rhythmic movements in different task variations and suggest a model consisting of rhythmic and discrete pattern generators that reproduces the major results. In the experiment, subjects performed single-joint elbow oscillatory movements (2 Hz). Upon a signal, they initiated a movement that consisted of a shift in the midpoint of the oscillation (MID), a shift in the amplitude of the oscillation (AMP), or a combination of both (MID + AMP). These shifting movements were performed either in a reaction time or in a self-paced fashion. The tendency for the EMG bursts associated with the discrete and rhythmic movements to synchronize was found similarly in all three tasks and instruction conditions, but the synchronization was most pronounced in the self-initiated discrete movement. Reaction time was increased for the combined task (MID + AMP), indicating higher control demands due to a combination of discrete and rhythmic components. This EMG burst synchronization was reproduced in a model based on a half-center oscillator with activation signals that produce either rhythmic or discrete activity. This activity was interpreted as torques driving a simple limb model. Summation of discrete and rhythmic activation signals of the pattern generators was sufficient to simulate the EMG burst synchronization. Further, simulation data reproduced the modulation of the reaction time as a function of the phase of the discrete movement.