In analyzing neurophysiologic data, individual experimental trials are usually assumed to be statistically independent. However, many studies employing functional imaging and electrophysiology have shown that brain activity during behavioral tasks includes temporally correlated trial-to-trial fluctuations. This could lead to spurious results in statistical significance tests used to compare data from different interleaved behavioral conditions presented throughout an experiment. We characterize trial-to-trial fluctuations in local field potentials recorded from the frontal cortex of a macaque monkey performing an oculomotor delayed response task. Our analysis identifies slow fluctuations (<0.1 Hz) of spectral power in 22/27 recording sessions. These trial-to-trial fluctuations are non-Gaussian, and call into question the statistical utility of standard trial shuffling. We compare our results with evidence for slow fluctuations in human functional imaging studies and other electrophysiologic studies in nonhuman primates.