The results of ab initio calculations have been utilized to produce plausible two-dimensional energy surfaces of the form V = a(x(1)(4) + x(2)(4)) + b(x(1)(2) + x(2)(2)) + cx(1)(2)x(2)(2) + dx(1)x(2) for the ring-puckering vibrations of bicyclo[3.3.0]oct-1,5-ene, with each coordinate representing the puckering motion of one ring. Polynomial expressions for the kinetic energy (reciprocal reduced mass) associated with the puckering motions of the rings were developed and utilized. These expressions were used together with the potential energy surfaces to calculate the quantum states and spectroscopic transitions for the puckering motions. The effect of varying the potential energy parameters c (ring-to-ring interaction) and d (cis-trans energy difference) on the energy levels and transitions was examined. The expected spectra are very rich and complex.