We have grown heterostructures based on low band-gap channels of Ga(x)In2-xSb (x = 0.5) and InAs(x)Sb1-x (x = 0.4-1) alloys, and characterized them using Hall measurements. For barrier layers, we used Al(x)In1-xSb (x = 1-0.5), with a composition chosen to be closely lattice matched to the channel layers, Ga(x)In1-xSb and InAs(x)Sb1-x. We also grew a Al(x)Ga1-xAs/GaAs(y)Sb1-y/GaAs pseudomorphic heterostructure, which is an analog of the In(x)Ga1-xAs pseudomorphic MODFET. In the case of Al(x)In1-xSb/Ga(x)In1-xSb and Al(x)In1-xSb/InAs(x)Sb1-x heterostructures, the barrier layers were undoped but we observed two-dimensional electron densities of about 7 x 10(11) to 2 x 10(12) cm-2 at 300 K. For the AlSb/InAs and Al0.7In0.3Sb/Ga0.7In0.3Sb heterostructures, the 300 K mobilities were 24,000 and 3000 cm2/V.s, respectively. Mobilities for the Al(x)In1-xSb/InAs(x)Sb1-x heterostructures were around 12,000 cm2/V.s. Hall measurements on the Al(x)Ga1-xAs/GaAs(y)Sb1-y/GaAs heterostructures indicated 2D electron densities of 3 x 10(12) cm-2 and mobilities of 3,000 cm2/V.s. These results indicate the potential of the Al(x)In1-xSb/InAs(x)Sb1-x (x = 0.4) heterostructures to be used as high-speed MODFETs and of the Al(x)Ga1-xAs/GaAs(y)Sb1-y/GaAs heterostructures to be used as power MODFETs.