Characteristic mode analysis (CMA) is based on time-harmonic electromagnetics and applied mostly in frequency domain. In this paper, CMA is extended to time domain (TD) for transmission problems. Based on the modal self- and mutual-admittance of two-port systems, the modal TD response is obtained using inverse fast Fourier transform, extrapolation and Hilbert transform. TD-CMA represents modal impulse response on specified ports, and impulse response of the system is the linear superposition of the modal ones. Numerical examples are provided to explain this new concept. For a pair of parallel wires, the calculated TD-CMA is alike the common and differential modes. For a pair of dipoles, TD-CMA can be divided into strong and weak coupling modes according to their magnitudes. The strong coupling modes are due to the pulse radiation and oscillations at dipole tips and feedings. Time delay paths are clearly observed in the near field but are not discernable in the intermediate field. This shows different coupling mechanisms for the two cases. TD-CMA expands research field of CMA and may find applications for analyzing transient behaviors of microwave systems.