Knowledge of the relative luminescence response to alpha and beta radiation is very important in TL and OSL dating. In the present study the relative alpha to beta response is studied in a sedimentary quartz sample, previously fired at 900 degrees C for 1 h, in the dose region between 1 and 128 Gy, for both thermoluminescence (T) and linearly modulated optically stimulated luminescence (LM - OSL). The LM OSL measurements were performed at room temperature and at 125 degrees C. All OSL signals were deconvolved into their individual components. Comparison of OSL curves after alpha and beta irradiation strongly supports that quartz OSL components follow first order kinetics in both cases. In the case of TL, the relative alpha to beta response is found to be very different for each TL glow-peak, but it does not depend strongly on irradiation dose. In the case of LM OSL measurements, it is found that the relative behaviour of the alpha to beta response is different for three distinct regions, namely the fast OSL component, the region of medium OSL component originating from the TL glow-peak at 110 degrees C when stimulation takes place at room temperature and finally the region of slow OSL component. Following stimulation at ambient temperature, the relative alpha to beta response of all components was not observed to depend significantly on dose, with the value of ratio being 0.03 and a tendency to decrease with increasing dose. However, in the case of measurements performed at 125 degrees C, the relative response of the fast components is much enhanced, and for the remaining components it increases with increasing dose. Special care must be taken to examine the relative alpha to beta response of the fast component at 125 degrees C which contrasts the relative response of the TL peak at ca. 325 degrees C. The implications for the dating of annealed quartz are also briefly discussed.