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We have investigated the growth of InAlGaN alloy thin films and InAlGaN/GaN quantum well (QW) heterostructures by rf plasma-assisted molecular beam epitaxy (RF-MBE). In-situ reflected high-energy electron diffraction (RHEED) was used to optimize the conditions for layer-by-layer growth and 0.25 μm thick InAlGaN layers exhibited very smooth surfaces with rms roughness of 0.7-1.0 nm. Sharp X-ray diffraction peaks with 2θ-widths as low as 3 times that of the commercial GaN template and ω-widths about the same as the GaN template evidence the good structural quality and compositional uniformity of the InAlGaN alloys. All the InAlGaN samples exhibited intense band-edge photoluminescence up to room temperature with linewidths as lows as 73 meV at 3.25 eV. The InAlGaN bandgap was characterized as a function of the In content, controlled by varying the growth temperature, and a large In-bowing coefficient of 8.4 eV was determined. A significant reduction of the polarization field in InAlGaN/GaN QWs was observed.