Electronic Journal of Differential Equations, Vol. 1998(1998), No. 18, pp. 1-6. Title: Some remarks on a second order evolution equation Author: Mohammed Aassila (Univ. Louis Pasteur et C.N.R.S., France) Abstract: We prove the strong asymptotic stability of solutions to a second order evolution equation when the LaSalle's invariance principle cannot be applied due to the lack of monotonicity and compactness. Submitted April 15, 1998. Published July 2, 1998. Math Subject Classification: 35B37, 35L70, 35B40. Key Words: asymptotic behavior; strong stabilization.