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The morphology of InGaN epilayers grown by metal-organic vapor phase epitaxy on GaN pseudosubstrates has been examined by atomic force microscopy. The composition of the epilayers has been measured using a combination of secondary ion mass spectrometry and x-ray photoelectron spectroscopy. The dependence of the growth mode on the growth conditions has been investigated. At the lowest temperatures and NH3 fluxes, a two-dimensional island nucleation growth mode is described, in which flat islands form stacks which align along underlying GaN terraces. As the growth temperature is increased a transition to a step-flow growth mode is observed. A transition from two-dimensional island nucleation to step-flow growth may also be achieved by increasing the NH3 flux, or by decreasing the trimethylindium flux. Each transition is discussed in terms of both surface kinetics and indium incorporation into the growing film. A transition from two-dimensional to three-dimensional growth may be induced by an increase in the growth rate. At high growth rates, three-dimensional nanostructures with a variety of shapes are observed suggesting that the growth is not in the Stranski-Krastanov mode. Instead, an increase in the overall reactor pressure is identified as a key factor in achieving Stranski-Krastanov growth.