For the short-term ultracapacitor models, first-, second-, third- and fourth-order transfer functions consistent with an RC ladder model are assumed. The transfer function coefficients are identified by a least squares algorithm based on experimental data consisting of time-varying current excitations and the resulting terminal voltage responses. A long-term model with six RC branches is developed by fitting the terminal voltage transient response to an impulse charging current. Hundreds of thousands of terminal voltage data points are recorded and least squares identification is employed to determine the optimal values of the unknown parameters in the long-term model. From the ultracapacitor models derived, terminal voltages under different current profiles can be determined accurately over the time frame of one hour with an error less than 0.1 V, the impulse charging and discharging response over a time frame of two months can be simulated with an error less than 0.08 V, and the instantaneous power available can be calculated