In this paper we construct Galois towers with good asymptotic properties over any non-
prime finite field F ; i.e., we construct sequences of function fields N = (N1,  N2,...  





)
over F of increasing genus, such that all the extensions Ni over N1 are Galois extensions and the
number of rational places of these function fields grows linearly with the genus. The limits
of the towers satisfy the same lower bounds as the best currently known lower bounds for
the Ihara constant for non-prime finite fields. Towers with these properties are important
for applications in various fields, including coding theory and cryptography.