Mixed Twistor D modules We introduce mixed twistor D modules and establish their fundamental functorial properties. We also prove that they can be described as the gluing of admissible variations of mixed twistor structures. In a sense mixed twistor D modules can be regarded as a twistor version of M. Saitos mixed Hodge modules. Alternatively they can be viewed as a mixed version of the pure twistor D modules studied by C. Sabbah and the author. The theory of mixed twistor D modules is one of the ultimate goals in the study suggested by Simpsons Meta Theorem and it would form a foundation for the Hodge theory of holonomic D modules which are not necessarily regular singular. Introduction Preliminary Canonical prolongations Gluing and specialization of r triples Gluing of good KMS r triples Preliminary for relative monodromy filtrations Mixed twistor D modules Infinitesimal mixed twistor modules Admissible mixed twistor structure and variants Good mixed twistor D modules Some basic property Dual and real structure of mixed twistor D modules Derived category of algebraic mixed twistor D modules Good systems of ramified irregular values