Using both observations and theoretical techniques, we show that the barred spiral galaxy NGC 3359 contains two pattern speeds. The faster pattern speed for the bar is obtained from isophotal analysis and stellar orbit theory. To explain the spiral arms and the observed velocity field of the disk, a slower pattern speed is required. Nonlinear resonance coupling is the supporting theory for the existence of two pattern speeds for the galaxy. The best match of our models with the observed data indicates a pattern speed for the bar of 39.17 km.sec(-1) approximately kpc(-1) and a value between 10 and 16 km.sec(-1).kpc(-1) for the spiral.