  We study two closely related operads: the Gelfand-Dorfman operad GD and the
Conformal Lie Operad CLie. The latter is the operad governing the Lie conformal
algebra structure. We prove Koszulity of the Conformal Lie operad using the
Groebner bases theory for operads and an operadic analogue of the Priddy
criterion. An example of deformation of an operad coming from the Hom
structures is considered. In particular we study possible deformations of the
Associative operad from the point of view of the confluence property. Only one
deformation, the operad which governs the identity $(\alpha(ab))c=a(\alpha
(bc))$ turns out to be confluent. We introduce a new Hom structure, namely
Hom--Gelfand-Dorfman algebras and study their basic properties.
