Neural receptive fields are plastic: with experience neurons in many brain regions change their spiking responses to relevant stimuli, Analysis of receptive field plasticity from experimental measurements is crucial for understanding how neural systems adapt their representations of relevant biological information. Current analysis methods using histogram estimates of spike rate functions in non-overlapping temporal windows do not track the evolution of receptive field plasticity on a fine time scale. Adaptive signal processing is an established engineering paradigm for estimating time-varying system parameters from experimental measurements. We present a new adaptive filter algorithm for tracking neural receptive field plasticity based on point process models of spike train activity. We derive an instantaneous steepest descent, recursive mode and particle filter algorithms using as the criterion function the instantaneous log likelihood of a point process spike train model. We apply the point process adaptive filter algorithm in a study of spatial (place) receptive field properties of simulated and actual spike train data from rat CA1 hippocampal neurons. The adaptive algorithm can update the place field parameter estimates on a millisecond time-scale. It reliably tracked the migration, changes in scale and changes in maximum firing rate characteristic of hippocampal place fields in a rat running on a linear track. Point process adaptive filtering offers a new analytic method for studying the dynamics of neural receptive fields.