Recoil-ion momentum distributions for two-photon double ionization of He and Ne (@! 44 eV) have been recorded with a reaction microscope at FLASH (the free-electron laser at Hamburg) at an intensity of 1 10 14 W=cm 2 exploring the dynamics of the two fundamental two-photon-two-electron reaction pathways, namely, sequential and direct (or nonsequential) absorption of the photons. We find strong differences in the recoil-ion momentum patterns for the two mechanisms pointing to the significantly different two-electron emission dynamics and thus provide serious constraints for theoretical models. DOI: 10.1103/PhysRevLett.101.073003 PACS numbers: 32.80.Rm, 41.60.Cr, 42.65.ÿk Since Einstein's revolutionary explanation of the photoelectric effect in 1905, the breakup of bound systems as a result of their interaction with single light quanta -the photons-has remained in the very focus of interest in experimental and theoretical physics as well as in chemistry and biology as one of the most fundamental reactions occurring in nature. Whenever there is more than one electron actively involved in the photoabsorption process, however, one faces serious problems in calculations as well as in measurements, even if only a single photon is absorbed at a time. Thus, the simplest situation where two electrons emerge from the He atom has numerically been solved only within the last decade when fully differential experimental cross sections have become available (see [1] for a review).Keeping the simple He target but increasing the number of photons, as, e.g., in strong-field double ionization at optical frequencies needing more than 50 quanta, still represents a serious challenge for computations (see, e.g., [2]). Likewise, kinematically complete experiments for this regime have been reported only within the last two months [3,4]. Also for the process of double ejection by Compton scattering, the comparison of experiment and theory does not go beyond the level of total cross sections [5].In this Letter we report the first differential measurement, recoil-ion momentum distributions, for the most basic nonlinear two-electron light-matter interaction, where two vacuum ultraviolet photons (44 eV each) ''simultaneously'' remove two electrons from He. The results are compared to the double ionization of Ne, where a sequential, stepwise absorption pathway with intermediate relaxation to a bound state of the Ne ion is energetically allowed. Vastly different momentum distributions are observed for both reactions and compared with theoretical predictions. Since the measured recoil-ion momentum spectra reflect the sum-momentum distributions of the emitted electrons and thus yield first information about the relative emission angles and the energy sharing between both electrons for different nonlinear processes, the data provide stringent test grounds for theoretical models. The experiments became feasible by exploiting a unique combination of modern multiparticle momentum imaging technique, ''reaction microscope' ' [6], and a novel light ...