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<p/> <p>This paper studies the stability of the solution <inline-formula> <graphic file="1029-242X-2011-979705-i1.gif"/></inline-formula> for a class of quasilinear implicit dynamic equations on time scales of the form <inline-formula> <graphic file="1029-242X-2011-979705-i2.gif"/></inline-formula>. We deal with an index concept to study the solvability and use Lyapunov functions as a tool to approach the stability problem.</p>