In this paper we report on the first demonstration, to the best of our knowledge, of continuous-wave (CW) difference-frequency generation (DFG) in LIS and LISe crystals in the mid-infrared between 5.5 and 11.3 mum. LiInSe2 provides a transparency range slightly shifted to longer wavelengths (to about 12 mum, instead of ~11 mum for LiInS 2), and its nonlinear susceptibility is ~1.6 times higher than that of LiInS2. While LiInS2 offers wider phase-matched spectral tuning. The high damage threshold combined with high thermal conductivity, broadband optical transparency and relatively high nonlinear optical coefficients makes LIS and LISe crystals attractive nonlinear optical materials for generation of powerful radiation in the deep mid-infrared by optical parametric interaction pumped with high laser power