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We prove almost global well-posedness for quasilinear strongly coupledwave-Klein-Gordon systems with small and localized data in two spacedimensions. We assume only mild decay on the data at infinity as well asminimal regularity. We systematically investigate all the possible quadraticnull form type quasilinear strong coupling nonlinearities, and provide a new,robust approach for the proof. In a second paper we will complete the presentresults to full global well-posedness.

Almost global well-posedness for quasilinear strongly coupled wave-Klein-Gordon systems in two space dimensions