Human subjects tracked sinusoidally moving visual targets with arm and eyes, in absence of visual feedback of the arm. The resulting frequency responses indicated that predictive mechanisms are involved both in arm and in eye tracking, and that the respective upper frequency limits are similar. Most importantly, substantial differences between arm and eye performance were observed: At low frequencies the gain of arm, but not of eye movement was consistently smaller than 0 dB. At higher frequencies arm, but not eye gain exhibited a marked amplitude non-linearity. The intra-trial gain and phase variability of arm movement was not correlated with the respective variability of eye movement. The reaction times to sudden changes of target parameters could be considerably different for arm and eye, and their inter-trial variability was not, or only marginally, correlated. Taken together, these findings strongly suggest that the mechanisms controlling predictive arm and eye movements in our experiment are organized to a major part in independent, parallel channels. The results are discussed with reference to a simple scheme of eye-arm coordination.