As defined by Keisler et al. in 1989, "hyperfinite" descriptiptive set theory studies internal, Borel, projective, and countably determined subsets of hyperfinite sets (in principle, also of *N) in a given nonstandard universe. The results obtained in this area are partially similar to those in the "Polish" DST, partially different, the proofs are usually very different. The talk will concentrate on the reducibility of Borel and countably determined equivalence relations in nonstandard domain.