Electronic Journal of Differential Equations, Vol. 2003(2003), No. 69, pp. 1-4. Title: On the composition conjectures Author: Mohamad A. M. Alwash (West Los Angeles College,CA, USA Abstract: We describe a class of polynomials that satisfy the composition conjecture for the moments. We also show that the composition conjecture for the moments is not weaker than the composition conjecture for a center. The problem is related to the centers of Abel differential equation. Submitted April 17, 2003. Published June 16, 2003. Math Subject Classifications: 34C25, 30E05. Key Words: Abel differential equation; center conditions; composition conjecture; moments.