We study the X-ray properties of LINER sources with definite detection of a broad H(alpha) emission line in their optical spectra, LINER 1s from Ho et al. sample. These objects preferentially harbor a low luminosity active nucleus at the center and show small or no intrinsic absorption (<10^(22) cm^(-1)). We analyzed all available X-ray archived XMM-Newton and Chandra observations of 13 LINER 1s satisfying the above criterion in a systematic homogeneous way. We looked for any correlations between the X-ray properties and the intrinsic parameters of our sample of LINER 1s. An absorbed power-law gave a good fit to the spectra of 9 out of the 13 sources. A thermal component and an absorbed power-law were required in the remaining 4 sources. We found a photon index between 1.3pm0.2 for the hardest source and 2.4^(+0.2)_(-0.3) for the softest one with a mean value of 1.9pm0.2 and a dispersion sigma=0.3. The thermal component had a mean temperature kT~0.6 keV. Significant short (hours to days) time-scale variability is not common in the present sample and was observed in only 2 sources (NGC 3226 and NGC 4278). Three other sources indicate a possible variability with a low K-S test probability (2%-4%) that the nuclear emission originates from a constant source. Significant variability on months to years time-scales is detected in 7 out of the 9 sources observed more than once. No significant Fe K(alpha) emission line at 6.4 keV was detected and upper limits were derived for the 4 sources with a high enough signal to noise ratio around 6 keV. Finally, we established, for the first time for a sample of LINER 1s, that the photon index is significantly anticorrelated to L_(2-10 keV)/L_(Edd). This anticorrelation is similar to the one seen in XRBs in their low/hard state where a radiatively inefficient accretion flow is thought to be responsible for the X-ray emitted energy.