Time dependent-measurements of the dynamic shear modulus in the splitting region a<->alpha + beta of poly(n-butyl methacrylate) (PnBMA) and poly(ethyl methacrylate) (PEMA) are reported. Non-equilibrium effects in the frequency-temperature region around the onset of the alpha transition are discussed. Physical ageing effects on the intensity, shape and position of the alpha and beta peaks of the shear loss modulus are reported. For the alpha relaxation a shift of the mean relaxation frequency to lower values, a peak sharpening, and an increase in intensity during ageing are observed, whereas the beta intensity decreases significantly. Long times are necessary to reach the equilibrium state a few kelvins below the onset temperature (approximate to glass transition temperature for PnBMA). A small amplitude fine structure was found in the frequency sweeps at temperatures below the onset temperature, which is discussed in terms of McCrum’s sequential ageing.