||The vertical transport properties of ac-driven weakly-coupled superlattices have been investigated experimentally in this thesis. These include the frequency-locking phenomena, the ac-induced generation and annihilation of self-sustained current oscillations (SSCOs), and the appearance of current steps in dynamic voltage bands (DVBs) which exhibit the period-adding bifurcations. In the study of the frequency-locking phenomena, it has been found that an ac-driven SSCO is frequency-locked into fac/n when the external ac frequency fac equals to nfo/m, where fo is the intrinsic frequency of the free SSCO and both n and m are integers with no common factors. In addition, a locking region for fac exists in the vicinity of nfo/m. As long as fac lies in this locking region, the frequency-locking into fac/n is observed. These phenomena are first explained qualitatively in terms of the limit cycle theory. Then a numerical simulation is performed using the discrete drift model. An excellent agreement between the experimental observations and the numerical results is obtained. The ac-induced generation of self-sustained current oscillations is manifested by the expansion of dynamical voltage bands upon applying an external ac signal. The width of a DVB increases with the increase of the ac amplitude while the ac frequencies are not much higher than the intrinsic ones. Quantitatively, the ac-induced expansion of DVBs is successfully simulated using the discrete drift model. Qualitatively, a discussion of related phase portraits in the phase space offers a straightforward way to account for this DVB expansion. Furthermore, when an ac signal with frequency much higher than the intrinsic one is applied, the width of a DVB shrinks with increasing ac frequencies, indicating the annihilation of SSCOs. The annihilation of SSCOs at high ac frequencies is ascribed to the ac-induced localization of domain walls. A series of current steps are observed in the dc current-voltage characteristics of DVBs under certain external ac driven conditions. On each current step the ac response is frequency locked to fac / n, where n is an integer larger than 1. When the applied ac frequency is equal to m X 3.6 KHz, where m is an integer and 3.6 KHz is close to the intrinsic frequency of free SSCOs within DVBs, these frequency-locked current steps are found to exhibit the so-called period-adding bifurcations represented by an arithmetical series of n = ml + 1, where l is an integer increasing from 1. The formation of the current steps in DVBs is explained based on the particular waveforms of the temporal current traces measured on current steps. The results in this thesis not only demonstrate the richness of the nonlinear dynamics of weakly-coupled superlattices, but also reveal in details the crucial role of an external ac signal in the vertical transport properties of superlattices.