Electronic Journal of Differential Equations, Vol. 2007(2007), No. 137, pp. 1-9. Title: On the solvability of a fourth order operator differential equations Author: Ahmed Nouar (Univ. de Skikda, Algeria) Abstract: We establish sufficient conditions for the solvability of a fourth order operator differential equation. These conditions are expressed in terms of operator coefficients. Submitted February 24, 2007. Published October 17, 2007. Math Subject Classifications: 47E05, 35K20. Key Words: Operator Pencil; operator differential equation; normal operator.