We experimentally carried out frequency conversion of a chirped and stretched up to 200 ps near-IR 90 fs Ti:Sapphire laser pulse into the mid-IR through difference frequency generation in either GaSe or LiGaS2 crystal. The crystal was pumped by laser radiation that passed through a BaWO4 crystal, where Stokes frequency-shifted radiation (signal wave) was generated through SRS. The generated ∼60 nJ mid-IR pulse had a central wavelength of 11.1 μm and FWHM spectral width of about 0.2 μm, which made it possible to achieve a pulse duration of ∼0.9 ps after its compression. The mid-IR pulse generation efficiency was ∼10−3% at SRS efficiency of 3%. To the best of our knowledge, this all solid-state scheme combining Raman shifting and second-order nonlinear crystals achieves the frequency down-conversion of femtosecond near-IR laser pulses to ∼11 μm radiation for the first time.