In this paper we report for the first time gas-source molecular beam epitaxy of both n- and p-channel InGaP/(In)GaAs modulation-doped heterostructure. The sheet density dependence of the two-dimensional hole gas (2DHG) mobility of p-type In0.49Ga0.51P/GaAs structures was investigated by Van der Paul Hall measurement at 300 and 77 K. The 2DHG densities of 1.78 x 10(12) and 1.03 x 10(12) cm(-2) with mobilities of 191 and 2831 cm(2)/V s at 300 and 77 K, respectively, for In0.49Ga0.51P/GaAs structures have been achieved. Low-temperature and high-magnetic field Hall measurements were also carried out. Longitudinal resistance of the structure shows two oscillations with different periods at 3 temperature of 0.3 It, indicating that, two subbands have been occupied by holes in the GaAs channel. The sheet density for each subband was estimated to be 1.22 x 10(12) and 0.77 x 10(12) cm, respectively. Both high hole mobility transistors (HHMTs) and high electron mobility transistors (HEMTs) were demonstrated. HHMTs show a maximum DC transconductance of 35 mS/mm. The saturation current is 57 mA/mm at 300 K with V-d = -3 V. Both extrinsic transconductance and saturation current of our novel In0.49Ga0.51P/GaAs HHMTs are well improved, compared with those of AlGaAs/GaAs and InGaAs/GaAs HHMTs. Enhanced-mode InGaP/InGaAs pseudomorphic HEMTs were achieved with a maximum DC transconductance of 250 mS/mm.