© 2015 The Institution of Engineering and Technology. In this study, the authors investigate the state response for continuous-time antilinear dynamical systems. First, they propose the concept of matrix anti-exponential function, and then derived some nice properties of this new function. With the matrix anti-exponential function as an effective tool, they obtain a closed-form expression for the state response of continuous-time antilinear systems. Finally, they derived an expression with finite terms for the proposed matrix antiexponential function, which will be useful for numerical implementation.