The behaviour of internal waves at a caustic level, turning point and critical layer have been investigated numerically. At a caustic reflection, a triad interaction was formed within the reflection region and the internal wave energy was transferred to lower frequencies (subharmonics). This resulted in a local subharmonic instability. One of the excited internal waves penetrated the caustic level and propagated downwards. This downward propagating wave then produced a second caustic where further reflection could take place. At a turning point, nonlinear interaction between the incident and reflected waves transferred energy to higher frequencies (evanescent trapped waves) which resulted in a superharmonic instability. At the critical level, energy was transferred to the mean flow. As the degree of nonlinearity increased, more energy was found to be transferred and overturning resulted due to a shear instability.