This nal project discusses some identities of the generalized Jacobsthal and Jacobsthal-Lucas sequences based on some properties such as D'ocagne's property, Catalan's property and Cassini's property or Simpson's property. Then it discusses the relationship between p(x)-Jacobsthal and p(x)-Jacobsthal-Lucas by the roots of and , also the proof of some identities of p(x)-Jacobsthal and p…