A full many-particle (beyond the mean-field approximation) electron quantum-transport simulator, which is named BITLLES, is used to analyze the transient current response of resonant tunneling diodes (RTDs). The simulations have been used to test an analytical (free-fitting parameters) small-signal equivalent circuit for RTDs under stable direct-current-biased conditions. The comparison provides an excellent agreement and furnishes a way to physically interpret each circuit element. In addition, a nonlinear novel RTD behavior in the negative differential conductance region has been established, i.e. asymmetric time constants in the RTD current response when high-low or low-high voltage steps are considered.