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Time-resolved piezoresponse force spectroscopy (TR-PFS) and spectroscopic imaging are developed to probe the spatial variability of relaxation behavior in nanoscale ferroelectric materials and structures. TR-PFS was applied to study polarization dynamics in polyvinylidine fluoride and trifluoroethylene nanomesas. We demonstrate that polarization relaxation in ferroelectric polymers is slow even on the ~10 nm length scale of piezoresponse force microscopy (PFM) signal generation. Furthermore, the relaxation times are found to be nonuniform within the nanomesa, indicative of a complex internal structure. The applicability of TR-PFM for studies of polarization dynamics in ferroelectric polymers and relaxors is discussed.