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This paper investigates the dependency of international stock market interaction on financial volatility. We show in a stylized economic model that volatility-dependent cross-market spillovers can be interpreted in two different ways, as indicating information flow or uncertainty. If higher volatility in one market leads to higher (lower) reactions in another market, volatility reflects information (uncertainty). We apply a simultaneous time-varying coefficient model, where structural ARCH-type variances serve two purposes: governing the time variation of spillovers and ensuring statistical identification. We analyze data of US and further stock markets. Indeed, we find strong nonlinear, volatility-dependent spillovers.