General considerations on the unification of A-type and B-type supersymmetries in the context of interacting p-branes strongly suggest that the signature of spacetime includes two timelike dimensions. This leads to the puzzle of how ordinary physics with a single timelike dimension emerges. In this letter we suggest that the two timelike dimensions could be real, and belong to two physical sectors of a single theory each containing its own timelike dimension. Effectively there is a single time evolution parameter. We substantiate this idea by constructing certain actions for interacting p-branes with signature (n, 2) that have gauge symmetries and constraints appropriate for a physical interpretation with no ghosts. In combination with related ideas and general constraints in S-theory, we are led to a cosmological scenario in which, after a phase transition, the extra timelike dimension becomes part of the compactified universe residing inside microscopic matter. The internal space, whose geometry is expected to determine the flavor quantum numbers of low energy matter, thus acquires a Minkowski signature. The formalism meshes naturally with a new supersymmetry in the context of field theory that we suggested in an earlier paper. The structure of this supersymmetry gives rise to a new Kaluza-Klein type mechanism for determining the quantum numbers of low energy families, thus suggesting that the extra timelike dimension would be taken into account in understanding the standard model of particle physics.