When moving grasped objects, people automatically modulate grip force (GF) with movement-dependent load force (LF) in order to prevent object slip. However, GF can also be modulated voluntarily as when squeezing an object. Here we investigated possible interactions between automatic and voluntary GF control. Participants were asked to generate horizontal cyclic movements (between 0.6 and 2.0 Hz) of a hand-held object that was restrained by an elastic band such that the load force (LF) reached a peak once per movement cycle, and to simultaneously squeeze the object at each movement reversal (i.e., twice per cycle). Participants also performed two control tasks in which they either only moved (between 0.6 and 2.0 Hz) or squeezed (between 1.2 and 4.0 Hz) the object. The extent to which GF modulation in the simultaneous task could be predicted from the two control tasks was assessed using power spectral analyses. At all frequencies, the GF power spectra from the simultaneous task exhibited two prominent components that occurred at the cycle frequency (e) and at twice this frequency (2e), whereas the spectra from the movement and squeeze control task exhibited only single peaks at e and 2e, respectively. At lower frequencies, the magnitudes of both frequency components in the simultaneous task were similar to the magnitudes of the corresponding components in the control tasks. However, as frequency increased, the magnitudes of both components in the simultaneous task were greater than the magnitudes of the corresponding control task components. Moreover, the phase relationship between the e components of GF and LF began to drift from the value observed in the movement control task. Overall these results suggest that, at lower movement frequencies, voluntary and automatic GF control processes operate at different hierarchical levels. Several mechanisms are discussed to account for interaction effects observed at higher movement frequencies.