The first phase of the seismically excited base-isolated benchmark building was received well by the structural control community, culminating in the March 2006 journal special issue. The special issue contained contributions from over dozen participants world-wide. While the focus of the Phase I effort was on linear isolation systems, Phase II attempts to galvanize research efforts on control of base-isolated buildings with nonlinear isolation systems. Primarily, friction and hysteretic lead–rubber-bearing (LRB) isolation systems are included in this effort. The superstructure and the control framework remains the same as the Phase I benchmark. The main difference will be in the nonlinear isolation systems used, and consequently the controllers necessary to control such systems. The primary objective of this paper is to present the Phase II benchmark problem definition along with a sample controller for friction isolation system. A sample controller for the LRB isolation system was presented earlier as a part of the Phase I special issue. Included in this paper is a broad set of carefully chosen performance measures, which remain the same as Phase I, so that the participants may evaluate their respective control designs. The control algorithms may be passive, active or semiactive. The benchmark structure considered in the Phase II study is an eight-story base-isolated building that is identical to the one considered for the Phase I study. The base isolation system consists of a combination of linear, nonlinear bearings and control devices. The superstructure is considered to be a linear elastic system with lateral–torsional behavior. The nonlinearities due to the isolators and control devices are limited to the isolation level only. A nonlinear dynamic analysis program and sample controllers are made available to the participants to facilitate direct comparison of results of different control algorithms. Copyright © 2008 John Wiley & Sons, Ltd.