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As magnetic recording density grows, the nonlinear distortions, known as transition shift and partial erasure,arise and limit the performance of the detector. In designing a detector, a phase detector is required to estimate the timing error in a timing recovery loop; the Muller & Mueller's phase detector is often adopted for its simple realization. In this article, we focus on the characteristics of the corresponding S-curve of the Muller & Mueller's phase detector in the presence of the non-linearities. In the presence of the partial erasure effect, the derived timing function is a suitable timing function with a decreased slope at the origin and it is a linear combination of two odd functions. One of the two functions is identical to that of a magnetic recording channel in the absence of the nonlinear distortions, and the other is itself a suitable candidate for a timing function. The transition shift causes a non-uniform shift of the S-curve with a different timing error. Computer simulations are given to verify these results.