The various alloys of gallium indium nitride (GaInN) form a technologically important semiconductor materials system, with potential uses in optoelectronic devices operating in the blue and blue-green region of the visible light spectrum. There has been little work reported on the growth of these materials, and this research addresses fundamental issues related to the epitaxial growth of the nitrides. Our first step in this project was to install an electron cyclotron resonance (ECR) apparatus into our molecular beam epitaxy system. This provided a source for atomic nitrogen needed to grow the nitride materials. We also put together a photoluminescence (PL) measurement system for optical characterization of the GaInN layers. In addition to PL, we also used X-ray diffraction and van der Pauw-Hall measurements to characterize the structural and carrier transport properties of the films;After the growth and characterization tools were in place, we embarked on a series of experiments to optimize the growth of Ga[subscript]0.8In[subscript]0.2N. The first step in this process was to gain some familiarity of the growth system and the characterization tools by growing a number of pure GaN layers. Using the information gained from these initial growths, we then employed a design-of-experiments (DOE) approach to quickly determine optimal growing conditions for Ga[subscript]0.8In[subscript]0.2N. One of the results of this exercise was somewhat surprising: The biggest factor in determining optical quality of the (Ga,In)N was the setting of the magnetic field which confines the plasma in the ECR nitrogen source. Following the optimization procedure, we grew a number of GaInN layers with different compositions, and mapped out a portion of the band gap vs. lattice constant contour for the nitride semiconductors;This work represents the first systematic study of GaInN, and the methods employed in our investigation will be useful in the eventual development of electronic and optoelectronics devices based on these materials.