Channel mismatches in time-interleaved analog-to-digital converters (TIADCs) typically result in significant degradation of the ADC's dynamic performance. Offset, gain, and timing mismatches have been widely investigated whereas nonlinearity mismatches have not. In this work, we analyze the influence of nonlinearity mismatches by using a polynomial model. As a cost measure we use the signal-to-noise and distortion ratio (SNDR) and then derive a compact formula describing the dependency on nonlinearity mismatches. Based on the spectral characteristics of the TIADCs, we propose a foreground estimation method and a compensation method using a cascaded structure of adders and multipliers. Through behavioral-level simulations, we prove the validity of the derivations and demonstrate that the proposed estimation and compensation method can bring a considerable amount of improvement in the combined TIADCs dynamic performance. The proposed method is efficient assuming that a smooth approximation of the nonlinearity mismatches is sufficient.