Abstract: We report on the thermal neutron flux measurements carried out at the Laboratorio Subterraneo de Canfranc (LSC) with two commercial 2 '' x 2 '' CLYC detectors. The measurements were performed as part of an experimental campaign at LSC with He-3 detectors, for establishing the sensitivity limits and use of CLYCs in low background conditions. Acareful characterization of the intrinsic alpha and gamma-ray background in the detectors was required and done with dedicated measurements. It was found that the alpha activities in the two CLYC crystals differ by a factor of three, and the use of Monte Carlo simulations and a Bayesian unfolding method allowed us to determine the specific alpha activities from the U-238 and Th-232 decay chains. The simulations and unfolding also revealed that the gamma-ray background registered in the detectors is dominated by the intrinsic activity of the components of the detector such as the aluminum housing and photo-multiplier and that the activity within the crystal is low in comparison. The data from the neutron flux measurements with the two detectors were analyzed with different methodologies: one based on an innovative alpha/neutron pulse shape discrimination method and one based on the subtraction of the intrinsic alpha background that masks the neutron signals in the region of interest. The neutron sensitivity of the CLYCs was calculated by Monte Carlo simulations with MCNP6 and GEANT4. The resulting thermal neutron fluxes are in good agreement with complementary flux measurement performed with He-3 detectors, but close to the detection limit imposed by the intrinsic a activity.