In this paper we study Lamé equations Ln,By=0 in so-called algebraic form, having only algebraic functions as solution. In particular we provide a complete list of all finite groups that occur as the monodromy groups, together with a list of examples of such equations. We show that the set of such Lamé equations with is countable, up to scaling of the equation. This result follows from the general statement that the set of equivalent second-order equations, having algebraic solutions and all of whose integer local exponent differences are 1, is countable.
The second author is supported by the Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO), the Netherlands, file number R 61-504, and by the Symbolic Analysis project of MITACS, Canada.