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During the years the investigation of the characteristic function of differential-difference polynomials is a long-cherished phenomenon and the results obtained in this direction can be viewed as a differential-difference analogue of the classical Valiron-Mokhon'ko Theorem (Year)and in this connection, it is necessary to investigate the deficiencies of some homogeneous differential-difference polynomials. Some characteristics of special differential-difference polynomials are also investigated and subsequent results on this topic can be estimated as differential-difference analogues of some classical results of Hayman and Yang (Year). Recently, with some groundworks on difference analogues of classical Nevanlinna's theory, there has been a renewed interest in the properties of complex difference and also meromorphic solutions of complex difference equations. By combining both complex differentials and difference, we discuss in this monograph about the deficiencies of differential-difference polynomials of meromorphic functions.