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In this paper, we give a complete geometric characterization of controlsystems, with m+1 inputs, locally static feedback equivalent to a triangularform compatible with the chained form, for m=1, respectively with the m-chainedform, for m>1. They are x-flat systems. We provide a system of first orderPDE's to be solved in order to find all x-flat outputs, for m=1, respectivelyall minimal x-flat outputs, for m>1. We illustrate our results by examples, inparticular by an application to a mechanical system: the coin rolling withoutslipping on a moving table.

Multi-input control-affine systems static feedback equivalent to a triangular form and their flatness