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Spectroscopy has attracted much attention in molecular detection, biomolecular identification, and chemical analysis for providing accurate measurement. However, it is almost unable to distinguish different sources with overlapped resonances in mixed analytes. Here, we present dual-comb delay spectroscopy to overcome this problem. The introduction of group delay spectroscopy provides a new tool to identify sources that would lead to overlapped resonances in intensity or phase spectroscopy. To obtain sufficiently high spectral resolution and signal-to-noise ratio for achieving reliable group delay spectrum, a probe comb with the wavelengths precisely scaned by a microwave source is applied, leading to attometer-level resolution and million-level signal-to-noise ratio. In an experiment, spectroscopy with an optional resolution up to 1 kHz (8 attometer), an average signal-to-noise ratio surpassing 2,000,000, and a span exceeding 33 nm is demonstrated. Two overlapped resonances from two different sources are clearly differentiated. Our work offers a new perspective for exploring the interaction between matter and light.