Edge emission characteristics of optically pumped GaN-AlGaN double heterostructures and quantum wells are examined. The samples, which were grown by metalorganic vapor phase epitaxy, are photoexcited with light from a pulsed nitrogen laser. The pump light is focused to a narrow stripe on the sample surface, oriented perpendicular to a cleaved edge, and the edge luminescence is collected and analyzed. We first compare emission characteristics of highly excited GaN-AlGaN double heterostructures grown simultaneously on SiC and sapphire substrates. Polarization resolved spectral properties of edge luminescence from both structures is studied as a function of pump intensity and excitation stripe length. Characteristics indicative of stimulated emission are observed, particularly in the sample grown on SiC. We then present results demonstrating laser emission from a GaN-AlGaN separate-confinement quantum-well heterostructure. At high pump intensities, band edge emission from the quantum well exhibits five narrow (∼1 Å) modes which are evenly spaced by 10Å to within the resolution of the spectrometer. This represents the first demonstration of laser action in a GaN-based quantum-well structure.