Abstract: In this paper authors introduced two new subclasses ∑_ϱτςξmp (α,β,η)and∑_ϱτςξmp^+▒〖(α,β,η)〗of meromorphically multivalent functions which aredefined by means of a new differential operator. By making use of the principle of differential subordination, authors investigate several inclusion relationships and properties of certain subclasses which are defined here by means of a differential operator. Some results connectedto subordination properties, coefficient estimates, convolutionproperties, integral representation, distortion theorems are obtained.We also extend the familiarconcept of (n,δ)-neighborhoods of analyticfunctions to these subclasses of meromorphicallymultivalentfunctions.