This is an Accepted Manuscript of an article published by Taylor & Francis as Marek, Fila, Bernhard Kawohl, and Howard A. Levine. "Quenching for Quasilinear Equations." Communications in Partial Differential Equations 17, no. 3-4 (1992): 593-614. Available online: https://doi.org/10.1080/03605309208820855. Posted with permission.</p