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Eclipsing binary systems with components that pulsate in gravity modes ($g$modes) allow for simultaneous and independent constraints of the chemicalmixing profiles of stars. We aim to assemble a sample of $g$-mode pulsators indetached eclipsing binaries with the purpose of finding good candidates forfuture evolutionary and asteroseismic modelling. In addition, we present a casestudy of the eclipsing binary KIC9850387, identified as our most promisingcandidate. We selected all of the detached eclipsing binaries in the Keplereclipsing binary catalogue and performed a visual inspection to determine thepresence and density of $g$ modes, and the presence of $g$-mode period-spacingpatterns in their frequency spectra. We then characterised our sample based ontheir $g$-mode pulsational parameters and binary and atmospheric parameters. Aspectroscopic follow-up of KIC9850387 was then performed. We then performedspectral disentangling followed by atmospheric modelling and abundance analysisfor the primary star. We utilised an iterative approach to simultaneouslyoptimise the pulsational and eclipse models, and subsequently performed ananalysis of the pressure- ($p$-) and $g$-mode pulsational frequencies. Wecompiled a sample of 93 Kepler eclipsing binary stars with $g$-mode pulsatingcomponents and identified clear $g$-mode period-spacing patterns in thefrequency spectra of seven of these systems. We found that the $g$-modepulsational parameters and the binary and atmospheric parameters of our sampleare weakly correlated at best. We find that the eclipsing binary KIC9850387 isa double-lined spectroscopic binary in a near-circular orbit with anintermediate-mass primary, and a solar-like secondary. We find $\ell=1$ and$\ell=2$ period-spacing patterns in the frequency spectrum of KIC9850387spanning more than ten radial orders each.

Tango of celestial dancers: A sample of detached eclipsing binary systems containing g-mode pulsating components. A case study of KIC9850387