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Let A and B satisfy the structural conditions (2), the local Hbhler contimdty interior to QffiGx(0, T) is proved for the generalized solutions of quasilinear parabolic equations as follows:ut -divA(~t,t,u, Vu)+ S(x,t,u, Vu) = 0

The HiSlder continuity is proved for the gradient of the solution Jo the one-sided obstacle problem of the following variational inequality in the case l~2. In [3] (also restricted to p>~2 ) other one-sided obstacle problem was considered and the CI,o regularity of the bounded solution is proved to

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