Plasma-assisted molecular beam epitaxial growth of Mg -doped GaN and InGaN on a sapphire substrate is investigated in this study. Electrical characteristics of p -type GaN strongly depend on the flux of Mg acceptors and the growth temperature. Only the intermediate range of Mg fluxes (beam equivalent pressures near 1×10^-9T) produce p -type GaN with good electrical properties, and a maximum hole concentration of 3.5 × 10¹⁸ cm^-3 is obtained with a Hall mobility of 2.1 cm²/V·s. Due to the strong surface accumulation of electrons, Hall measurements do not indicate p -type polarity for In fraction beyond 11%. In contrast, hot probe measurements show that p -polarity can be measured for the entire range of Mg -doped In mole fractions. Electroluminescence also indicates p -polarity for Ga -rich mole fractions. In _x Ga_{1- x} N p - n homojunctions are fabricated and tested. All GaN devices show low series resistance (0.03 ohm-cm²) and insignificant parasitic leakage. IV curves of all three InGaN homojunctions show rectifying characteristics under dark conditions and photo-response under outdoor sunlight, indicating the existence of holes in InGaN with up to 40% In content.