  We study classical chaotic motions in the Berenstein-Maldacena-Nastase (BMN)
matrix model. For this purpose, it is convenient to focus upon a reduced system
composed of two-coupled anharmonic oscillators by supposing an ansatz. We
examine three ans\"atze: 1) two pulsating fuzzy spheres, 2) a single
Coulomb-type potential, and 3) integrable fuzzy spheres. For the first two
cases, we show the existence of chaos by computing Poincar\'e sections and a
Lyapunov spectrum. The third case leads to an integrable system. As a result,
the BMN matrix model is not integrable in the sense of Liouville, though there
may be some integrable subsectors.
