We present measurements of the nanoscale elastic and viscoelastic properties of samples of poly(methylmetacrylate) (PMMA)/rubber nanocomposites. For these studies we have used a new technique based on atomic force microscopy (AFM) with ultrasonic excitation, heterodyne force microscopy (HFM), which provides a means of testing the viscoelastic response of polymeric materials locally (in tip-probed regions) at MHz frequencies. Phase-HFM contrast distinguishes local differences in the dynamic response of PMMA/rubber composites. Comparison of HFM with other AFM-based techniques (ultrasonic force microscopy, friction force microscopy and force modulation microscopy), while imaging the same surface region, emphasizes the unique capabilities of HFM for these kinds of studies, and reveals key nanostructural characteristics of the composites. Some of the toughening particles appear to be broken down, with areas of PMMA detached from the surrounding matrix.