Steady-state visually evoked potentials (SSVEPs) are widely used to index top-down cognitive processing in human electroencephalogram (EEG) studies. Typically, two stimuli flickering at different temporal frequencies (TFs) are presented, each producing a distinct response in the EEG at its flicker frequency. However, how SSVEP responses in EEGs are modulated in the presence of a competing flickering stimulus just because of sensory interactions is not well understood. We have previously shown in local field potentials (LFPs) recorded from awake monkeys that when two overlapping full-screen gratings are counterphased at different TFs, there is an asymmetric SSVEP response suppression, with greater suppression from lower TFs, which further depends on the relative orientations of the gratings (stronger suppression and asymmetry for parallel compared with orthogonal gratings). Here, we first confirmed these effects in both male and female human EEG recordings. Then, we mapped the response suppression of one stimulus (target) by a competing stimulus (mask) over a much wider range than the previous study. Surprisingly, we found that the suppression was not stronger at low frequencies in general, but systematically varied depending on the target TF, indicating local interactions between the two competing stimuli. These results were confirmed in both human EEG and monkey LFP and electrocorticogram (ECoG) data. Our results show that sensory interactions between multiple SSVEPs are more complex than shown previously and are influenced by both local and global factors, underscoring the need to cautiously interpret the results of studies involving SSVEP paradigms.SIGNIFICANCE STATEMENT Steady-state visually evoked potentials (SSVEPs) are extensively used in human cognitive studies and brain-computer interfacing applications where multiple stimuli flickering at distinct frequencies are concurrently presented in the visual field. We recently characterized interactions between competing flickering stimuli in animal recordings and found that stimuli flickering slowly produce larger suppression. Here, we confirmed these in human EEGs, and further characterized the interactions by using a much wider range of target and competing (mask) frequencies in both human EEGs and invasive animal recordings. These revealed a new "local" component, whereby the suppression increased when competing stimuli flickered at nearby frequencies. Our results highlight the complexity of sensory interactions among multiple SSVEPs and underscore the need to cautiously interpret studies involving SSVEP paradigms.