A six-story seismically isolated structure fitted with semiactive hydraulic devices is analyzed in order to study the effect of time lag in the devices and mass eccentricity in the superstructure on the lateral-torsional behavior. The computer program 3DBASIS, which allows the nonlinear dynamic analysis of three-dimensional structures, is used in this work. Appropriate modifications were made to this program to incorporate the behavior of semiactive hydraulic devices. Three different types of base isolation systems were considered: (1) lead rubber bearings; (2) lead rubber bearings with supplemental viscous damping; and (3) lead rubber bearings with semiactive viscous damping. A comparison of these three base-isolation systems, considering both the effects of eccentricity in the structure and differential time lags in semiactive hydraulic devices are studied. The peak isolator shear, isolation drift, rotation, and torsional moment are reported. Three major earthquake motion records, namely, the El Centro record of the 1940 Imperial Valley earthquake, the Meloland record of the 1979 Imperial Valley earthquake, and the Sylmar free field record of the 1994 Northridge earthquake were used as inputs in the analyses.