Electronic Journal of Differential Equations, Vol. 1999(1999), No. 26, pp. 1-19. Title: Periodic traveling waves for a nonlocal integro-differential model Author: Peter Bates (Brigham Young Univ., Provo, UT, USA) Fengxin Chen (Univ. of Texas at San Antonio, TX, USA) Abstract: We establish the existence, uniqueness and stability of periodic traveling wave solutions to an intrego-differential model for phase transitions. Submitted June 15, 1999. Published August 19, 1999. Math Subject Classifications: 35K55, 35Q99 Key Words: nonlocal phase transition; periodic traveling waves; stability.