Context. Variability is a general property of active galactic nuclei (AGN). The way in which these changes occur at X-rays is not yet clearly understood. In the particular case of low-ionization nuclear emission line region (LINER) nuclei, variations on the timescales from months to years have been found for some objects, but the main driver of these changes is still debated. Aims: The main purpose of this work is to investigate the X-ray variability in LINERs, including the main driver of these variations, and to search for possible differences between type 1 and 2 objects. Methods: We examined the 18 LINERs in the Palomar sample with data retrieved from the Chandra and/or XMM-Newton archives that correspond to observations gathered at different epochs. All the spectra for the same object were fitted simultaneously to study long-term variations. The nature of the variability patterns were studied by allowing different parameters to vary during the spectral fit. Whenever possible, short-term variations from the analysis of the light curves and long-term UV variability were studied. Results: Short-term variations are not reported in X-rays. Three LINERs are classified as non-AGN candidates in X-rays, all of them are Compton-thick candidates; none of them show variations at these frequencies, and two of them vary in the UV. Long-term X-ray variations were analyzed in 12 out of 15 AGN candidates; about half of them showed variability (7 out of the 12). At UV frequencies, most of the AGN candidates with available data are variable (five out of six). Thus, 13 AGN candidates are analyzed at UV and/or X-rays, ten of which are variable at least in one energy band. None of the three objects that do not vary in X-rays have available UV data. This means that variability on long-timescales is very common in LINERs. These X-ray variations are mainly driven by changes in the nuclear power, while changes in absorptions are found only for NGC 1052. We do not find any difference between type 1 and 2 LINERs, neither in the number of variable cases (three out of five type 1 and four out of seven type 2 LINERs), nor in the nature of the variability pattern. We find indications of an anticorrelation between the slope of the power law, Γ, and the Eddington ratio. Conclusions: LINERs are definitely variable sources irrespective of whether they are classified as optical type 1 or 2. Their BH masses, accretion rates, and variability timescales place them in the same plane as more powerful AGN at X-rays. However, our results suggest that the accretion mechanism in LINERs may be different. UV variations of some type 2 LINERs were found, this could support the hypothesis of a torus that disappears at low luminosities. Appendices are available in electronic form at http://www.aanda.org