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Work is reported on composites comprising either epoxy resin or crosslinked polyethylene (XLPE) filled with silica nanoparticles (surface functionalisated and unfunctionalisated). Measurements were made of the dielectric spectra, charging and discharging currents under high electric fields, and space charge dynamics using the pulsed electroacoustic (PEA) technique. Considerable studies were made of the effect of humidity on epoxy nanocomposites. It was found that the epoxy composites filled with nanoparticles could absorb up to 60% more water by weight than the unfilled epoxy. For composites filled with microparticles, nearly all the water was absorbed by the resin. The glass transition temperature (Tg) for all epoxy samples, measured by both differential scanning calorimetry (DSC) and dielectric spectroscopy, showed a monotonic reduction with increase of hydration resulting in a 20K decrease for fully hydrated samples. This led to the conclusion that the extra hydration found in the nanocomposites was not in the bulk resin but was likely to be located on the surface of the nanoparticles. This is further supported by measurement of the hydration isotherms at room temperature and the resultant swelling as a function of humidity. A "water shell" model is developed in which there is an inner layer of approximately 5 – 10 bound water molecules on the surface of the nanoparticles, a further layer, approximately 25nm thick, in which water is in sufficient concentration to allow conduction, and an outer layer, approximately 50nm thick, which cannot support true conduction (i.e. the continuous movement of charge carriers.) This model is used to explain the sub-hertz dielectric results (in terms of percolation limited conduction) as well as those at around 1 – 10Hz that indicate the presence of bound or free water.