We report the first successful monitoring of two Sgr A* flares in the X-ray, NIR, and submillimeter bands. The flares were observed on 2005 July 31 and 2006 July 17 using Chandra, Keck, SMA, and CSO. The NIR amplitudes and spectral indices of both flares appeared similar to those of previous flares, although Keck missed the peak of the 2006 flare by about 30 minutes. The submillimeter flares were likewise of similar amplitudes. However, the submillimeter peak of the 2006 flare lagged the shorter wavelengths by nearly 100 minutes, while the lag of the submillimeter peak in 2005 appears to have been about 80 minutes shorter. Remarkably, the 2006 flare shows a strong X-ray flare, while the 2005 flare has no detectable X-ray emission above the constant background in the central parsec. Thus, the two flares have very different X-ray to NIR flux ratios and submillimeter lags. Using synchrotron theory and an expanding relativistic plasma model, we propose a possible correlation between the X-ray to NIR flux ratios and the time lags of the submillimeter peaks in the two flares. Future accretion/flare models will have to match both the broadband SED and the temporal evolution of these flares.