We study the global and local motion in a barred galaxy model with a massive nucleus. The local model is made up of a two-dimensional perturbed harmonic oscillator and can be derived by expanding the global model in the vicinity of a stable Lagrange point. Low- and high-energy stars in the global model display chaotic motion. Comparison with previous work shows that, for the chaotic motion of low-energy stars, the massive nucleus is responsible. In the local motion, low-energy stars show resonance phenomena while the chaotic phenomena, if any, are negligible. On the other hand, the high-energy stars do not show bounded motion in the local model. This is an indication of particular activity near the centre of galaxies with massive nuclei.