Separation of the three-dimensional Helmholtz equation in elliptic coordinates leads to the Lamé wave equation
where h, separation constants. In § 2, the spectrum of equation (1) and the Lamé wave functions are defined and a survey on known results is given. The Klein-Bocher classification of linear second order equations with rational coefficients is presented and the position of equation (1) is indicated. In § 3, the asymptotics of the solutions in the complex z-plane are studied for arbitrary complex parameter values k,h,. In § 4, the asymptotics of the spectrum and of the angle wave functions are studied by passing to the complex domain. For the spectral parameters h, a system of equations , , is obtained where the are integers which are generalizations of the classical Bohr-Sommerfeld quantization law. The functions are periods of the hyperelliptic integral .