  We report here a systematic study of the energy gaps at the odd-integer
quantum Hall states $\nu=3$ and 5 under tilted magnetic (B) fields in a high
quality Si two-dimensional electron system. Out of the coincidence region, the
valley splitting is independent of the in-plane B fields. However, the $\nu=3$
valley gap differs by about a factor of 3 ($\Delta_v\sim$ 0.4K vs. 1.2K) at
either side of the coincidence. More surprisingly, instead of reducing to zero,
the energy gaps at $\nu=3$ and 5 rise rapidly when approaching the coincidence
angles. We believe that such anomaly is related to strong coupling of the
nearly degenerate Landau levels.
