The recurrence and birecurrence property in Finsler space have been studied by the Finsleriangeometrics. The aim of this paper is to obtain the necessary and sufficient condition for Cartan’s secondcurvature tensor that is recurrnt and birecurrent in generalized BP−recurrent space and generalizedBP−birecurrent space, respectively. We discuss certain identities belong to the mentioned spaces. Further,we end up this paper with some illustrative examples.