Infrared spectroscopic observations of LL Andromedae and EF Eridani are presented .
Our K band spectrum of LL Andromedae reveals the presence of methane absorption in the secondary star indicating an effective temperature \lesssim 1300K , similar to a “ T ” type methane brown dwarf .
The secondary star in EF Eridani is seen to be warmer with an effective temperature of \sim 1650K and a spectroscopic classification consistent with an L4-5 star .
Both secondaries have theoretical mass estimates of 0.04-0.055 M _ { \odot } ( 40-55 M _ { Jupiter } ) .
Our IR spectroscopic observations of LL And and EF Eri provide the first direct proof of the theoretical prediction that post-period minimum cataclysmic variables contain brown dwarf-like secondary stars .