U.S. trading in non-U.S. stocks has grown dramatically. Round-the-clock, these stocks trade in the home market, in the U.S. marketand, potentially, in both markets simultaneously. We use a state space model to study 24-hour price discovery. As opposed to thestandard variance ratio'' approach, this model deals naturally with (i) simultaneous quotes in an overlap, (ii) missing observations in anon-overlap, (iii) noise due to transitory microstructure effects, and (iv) contemporaneous correlation in returns due to market-widefactors. For NYSE-listed Dutch stocks, home market hours are a factor three more informative than U.S. market hours, which, inturn, are twice as informative as overnight hours. Surprisingly, strongest price discovery takes place in the NYSE preopening. Themodel shows results that are significantly different from the variance ratio approach.