Resolution and bandwidth are critical for cavity-enhanced dual-comb spectroscopy (CE-DCS). Here, we pioneer an adaptive approach in CE-DCS to improve the broadband as well as the resolution. Postcorrections to dual-comb interferograms adaptively compensate the relative phase jitters of the optical frequency combs and result in both a mode-resolved spectral resolution and a signal-to-noise ratio of 440:1 in 1 s. Meanwhile, an adaptive comb-cavity locking scheme exploits more than 90% of the comb modes, covering 340cm 1 (10 THz) at 6450cm 1. For a single dual-comb interferogram, more than 40,000 comb teeth spaced by 250 MHz are measured in less than 7.5 ms, contributing to a noise equivalent absorption per spectral element of 2×10 10cm 1·Hz 1/2. This adaptive cavity-enhanced dual-comb spectroscopy technique provides an attractive spectroscopic tool that may be utilized in trace-gas sensing, breath and cancer analysis, and engine combustion diagnosis.