The use of transversal filters for automatic equalization has made possible high-speed data communication over voiceband telephone channels. Recently much attention has been focused on the possible use of the high-speed data sets in private line multiparty polling systems. However, for such applications, it is necessary to reduce the start-up time of the present automatic equalizer drastically. This paper examines the start-up time (settling time) of the transversal filter equalizer for two important classes of data communication systems: Class IV partial-response systems and single-sideband Nyquist systems. (The latter represents the limiting case of vestigial-sideband systems with small roll-off bandwidth.) It is shown that in single-sideband Nyquist systems the input signals to the gain controls of the transversal equalizer may be nearly orthonormal. Consequently the equalizers may have a short settling time. It is also shown that the equalizer settling time is much longer in Class IV partial-response systems, because such systems use controlled intersymbol interference and the input signals to the gain controls are highly correlated. The possibility of reducing the settling time of the automatic equalizers is examined. A new equalizer structure is developed based on the following principles: (i) Equalizer settling time can be minimized by making the input signals to the gain controls orthonormal, and (ii) Such a minimization does not change the noise power, the mean-square equalization error, the convexity of the gain control adjustment, and the feedback control loops in the equalizer. These principles are general in that they apply regardless of the type of modulation — single-, vestigial-, or double-sideband (SSB, VSB, or DSB) — or the signaling scheme (Nyquist or partial-response). Application of these principles to Class IV partial-response systems is considered. For private line systems and systems where amplitude distortions in the communication channels are not severe (delay distortions can be arbitrary), the new equalizer can be implemented by simply adding a prefixed weighting matrix to the conventional transversal equalizer. Analysis and computer simulation show that the use of such a new equalizer can residt in a significant reduction in the system's start-up time.