Very highly efficient GaAs-AlGaAs GRIN-SCH lasers were grown on an n-GaAs substrate as well as on a semi-insulating GaAs substrate by MBE. The threshold current density J//t//h of the lasers was found to be minimum when the thickness of the GaAs quantum well active layer is 6 nm. The lowest J//t//h of 260 A/cm**2 was achieved for the broad-area Fabry-Perot laser (the Al composition of the cladding layer x equals 0. 7, the cavity length L equals 400 mu m). A ridge-waveguide (5 mu m wide stripe) GaAs-AlGaAs GRIN-SCH laser, which is monolithically integrated with GaAs MESFET's on a semi-insulating GaAs substrate, exhibited cw operation with a threshold current as low as 19 mA at room temperature.