In this paper we define two generalisations of Dirac operators for Drinfeld's Hecke algebra. One generalisation, Parthasarathy operators inherit the notion of the Dirac inequality. The second generalisation, Vogan operators, inherit Dirac cohomology; if an operator has non-zero cohomology then it relates the infinitesimal character with a character of the a group. We prove properties about these operators and give a family of operators in each class.