A central goal of systems neuroscience is to develop accurate quantitative models of how neural circuits process information. Prevalent models of light response in retinal ganglion cells (RGCs) usually begin with linear filtering over space and time, which reduces the high-dimensional visual stimulus to a simpler and more tractable scalar function of time that in turn determines the model output. Although these pseudo-linear models can accurately replicate RGC responses to stochastic stimuli, it is unclear whether the strong linearity assumption captures the function of the retina in the natural environment. This paper tests how accurately one pseudo-linear model, the generalized linear model (GLM), explains the responses of primate RGCs to naturalistic visual stimuli. Light responses from macaque RGCs were obtained using large-scale multi-electrode recordings, and two major cell types, ON and OFF parasol, were examined. Visual stimuli consisted of images of natural environments with simulated saccadic and fixational eye movements. The GLM accurately reproduced RGC responses to white noise stimuli, as observed previously, but did not generalize to predict RGC responses to naturalistic stimuli. It also failed to capture RGC responses when fitted and tested with naturalistic stimuli alone. Fitted scalar nonlinearities before and after the linear filtering stage were insufficient to correct the failures. These findings suggest that retinal signaling under natural conditions cannot be captured by models that begin with linear filtering, and emphasize the importance of additional spatial nonlinearities, gain control, and/or peripheral effects in the first stage of visual processing.