2005-Oujda International Conference on Nonlinear Analysis, Oujda, Morocco. Electronic Journal of Differential Equations, Conference 14 (2006), pp. 119-124. Title: Fast and heteroclinic solutions for a second order ODE Author: Margarita Arias (Univ. de Granada, Spain) Abstract: We present some results on the existence of fast and heteroclinic solutions of an ODE connected with travelling wave solutions of a Fisher-Kolmogorov's equation. In particular, we present a variational characterization of the minimum speed of propagation. Published September 20, 2006. Math Subject Classifications: 34C37, 35K57, 49J35. Key Words: Fisher-Kolmogorov's equation; travelling wave solutions; speed of propagation; variational methods; constrained minimum problem.