Earlier work on sector bounded nonlinear multivariable systems has provided dynamic performance bounds on system response, via an element-by-elementL∞treatment. However, this approach relies on a stability criterion which is potentially very conservative, since it ignores both frequency dependence and phase interrelationships. In the paper, we useL2vector norms in conjunction with nonsimilarity scaling to retrieve this information, and hence to derive a significantly improved stability condition. By the introduction of exponential weighting, it is then shown that theL2stability result may be used to establish absolute bounds on system performance.