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In the present paper, we introduce a new family of $  \theta-$methods for solving delay differential equations. New methods aredeveloped using a combination of decomposition technique viz. new iterativemethod proposed by Daftardar Gejji and Jafari and existing implicit numericalmethods. Using Butcher tableau, we observed that new methods are nonRunge-Kutta methods. Further, convergence of new methods is investigated alongwith its stability analysis. Applications to variety of problems indicates thatthe proposed family of methods is more efficient than existing methods.

A New family of methods for solving delay differential equations