  In this paper, we generalize the embedded homology groups of hypergraphs
initially given in [S. Bressan, J. Li, S. Ren, and J. Wu, The embedded homology
of hypergraphs and applications, Asian J. Math. 23(3)(2019) 479-500] and study
the relative embedded homology groups of hypergraph pairs. We prove some long
exact sequences as well as a Mayer-Vietoris sequence for the relative embedded
homology groups of hypergraph pairs. Moreover, we briefly discuss the
two-dimensional persistence for the relative embedded homology groups of
hypergraph pairs.
