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We study the ``normal'' decay phase of the X-ray afterglows of gamma-raybursts (GRBs), which follows the shallow decay phase, using the eventssimultaneously observed in the R-band. The classical external shock model -- inwhich neither the delayed energy injection nor time-dependency of shockmicro-physics is considered -- shows that the decay indices of the X-ray andR-band light curves, $\alpha_{\rm X}$ and $\alpha_{\rm O}$, obey a certainrelation, and that in particular, $\alpha_{\rm O}-\alpha_{\rm X}$ should belarger than -1/4 unless the ambient density increases with the distance fromthe central engine. For our selected 14 samples, we have found that 4 eventsviolate the limit at more than the 3$\sigma$ level, so that a fraction ofevents are outliers of the classical external shock model at the ``normal''decay phase.

Testing the External Shock Model of Gamma-Ray Bursts using the Late-Time Simultaneous Optical and X-ray Afterglows