We study the asymptotic behavior of the zeros of a two-frequency-scale transfer function in terms of the zeros of its slow and fast transfer functions. By introducing the notion of type index, we will show that all zeros of a two-frequency-scale transfer function with the type index of either upsilon greater than or equal to 0 or upsilon=-1 can be completely characterized in a manner that is quite similar to the characterization of the poles. We also give a partial characterization for all other zeros in terms of the cardinality of their zero sets.