Title: Resonances for Microstrip Transmission Lines Faouzi M. Triki Department of Mathematics Michigan State University East Lansing, MI 48824-1027 E-mail: triki@math.msu.edu Web page: http://www.math.msu.edu/~triki/ Abstract: In this paper we discuss resonance problems inherent in microstrip transmission lines mounted on planar open waveguides. Microstrip transmission lines are widely used in printed-circuit technology and antenna industry. Since microstrip transmission lines are highly resonant structures, an accurate determination of resonances is of great importance. Our aim in this work is to rigorously derive asymptotic formulae for resonances associated with the full Maxwell's equations in a microstrip transmission line mounted on a planar open waveguide when the width of the microstrip transmission line goes to zero.