Similar behavioral deficits are shared between individuals with autism spectrum disorders (ASD) and their first-degree relatives, such as impaired face memory, object recognition, and some language aspects. Functional neuroimaging studies have reported abnormalities in ASD in at least one brain area implicated in those functions, the fusiform gyrus (FG). High frequency oscillations have also been described as abnormal in ASD in a separate line of research. The present study examined whether low- and high-frequency oscillatory power, localized in part to FG and other language-related regions, differs in ASD subjects and first-degree relatives. Twelve individuals with ASD, 16 parents of children with ASD, and 35 healthy controls participated in a picture-naming task using magnetoencephalography (MEG) to assess oscillatory power and connectivity. Relative to controls, we observed reduced evoked high-gamma activity in the right superior temporal gyrus (STG) and reduced high-beta/low-gamma evoked power in the left inferior frontal gyrus (IFG) in the ASD group. Finally, reductions in phase-locked beta-band were also seen in the ASD group relative to controls, especially in the occipital lobes (OCC). First degree relatives, in contrast, exhibited higher high-gamma band power in the left STG compared with controls, as well as increased high-beta/low-gamma evoked power in the left FG. In the left hemisphere, beta- and gamma-band functional connectivity between the IFG and FG and between STG and OCC were higher in the autism group than in controls. This suggests that, contrary to what has been previously described, reduced connectivity is not observed across all scales of observation in autism. The lack of behavioral correlation for the findings warrants some caution in interpreting the relevance of such changes for language function in ASD. Our findings in parents implicates the gamma- and beta-band ranges as potential compensatory phenomena in autism relatives.