Abstract. We give two tests for transcendence of Mahler functions. For our first, we introduce the notion of the eigenvalue λ F of a Mahler function F (z), and develop a quick test for the transcendence of F (z) over C(z), which is determined by the value of the eigenvalue λ F . While our first test is quick and applicable for a large class of functions, our second test, while a bit slower than our first, is universal; it depends on the rank of a certain Hankel matrix determined by the initial coefficients of F (z). We note that these are the first transcendence tests for Mahler functions of arbitrary degree. Several examples and applications are given.