The dynamical properties of longitudinal and transverse conduction of NbSe$_3$ single-crystals have been simultaneously studied when the current is applied along the b axis (chain direction). In the vicinity of the threshold electric field for CDW sl
iding, the transverse conduction sharply decreases. When a rf field is applied, voltage Shapiro steps for longitudinal transport are observed as usual, but also current Shapiro steps in the transverse direction. The possible mechanisms of this effect are discussed.
We report transport measurements under very high current densities $j$, up to $sim10^8$~A/cm$^2$, of quasi-one-dimensional charge-density wave (CDW) conductors NbSe$_3$ and TaS$_3$. Joule heating has been minimized by using a point-contact configurat
ion or by measuring samples with extremely small cross-sections. Above $j_c approx 10^7$~A/cm$^2$ we find evidence for suppression of the Peierls gap and development of the metallic state. The critical CDW velocity corresponding with $j_0$ is comparable with the sound velocity, and with $Delta/ hbar k_F$ ($k_F$ is the Fermi wave vector), which corresponds to the depairing current. Possible scenarios of the Peierls state destruction are discussed.
