  The Floquet eigenvalue problem and a generalized form of the Wangerin
eigenvalue problem for Lam\'e's differential equation are discussed. Results
include comparison theorems for eigenvalues and analytic continuation, zeros
and limiting cases of (generalized) Lam\'e-Wangerin eigenfunctions. Algebraic
Lam\'e functions and Lam\'e polynomials appear as special cases of
Lam\'e-Wangerin functions.
