Lattice-matched Ga0.51In0.49P/GaAs and strained Ga0.51In0.49P/InxGa1-xAs/GaAs (0.1 less than or equal to x less than or equal to 0.25) modulation-doped field-effect transistor structures were grown by gas source molecular beam epitaxy by using Si as dopant. Detailed electrical characterization results are presented, The Ga0.5In0.49P/In0.25Ga0.75As/GaAs sample yielded dark two-dimensional electron gas densities of 3.75 x 10(12) cm(-2) (300 K) and 2.3 x 10(12) cm(-2) (77 K) which are comparable to the highest sheet electron densities reported in AlGaAs/InGaAs/GaAs and InAlAs/InGaAs/InP modulation-doped heterostructures. Persistent photoconductivity was observed in the strained samples only. A 0.797 eV deep lever has been detected in the undoped GaInP layers of the structures. Another lever, with DLTS peak height dependent an the filling pulse width, has been detected at the interface of the strained samples. Based on the DLTS and Hall effect measurement results, this level, which seems to be the origin of persistent photoconductivity, can be attributed to the strain relaxation related defects.