This paper presents a proposal for filtering electrooculogram signals using the Discrete Wavelet and the Discrete Wavelet Packet Transforms. We compare our proposal with other digital filters commonly used for this type of biological signals, evaluating the results in terms of signal-to-noise ratio improvement, energy, correlation coefficient and mean absolute error reduction. For the analyzed cases, the wavelet and wavelet packet approaches improve considerably the results obtained with digital filters. Moreover, we also provide the most suitable parameters for the wavelet and the wavelet packet analysis.