The holotype female of Andrassya tundrovi Gagarin, 1993 is re-examined. Malakhovia chernobyli gen. n., sp. n. from the water reservoir (cooler) of Chernobyl Atomic Energy Station (northern Ukraine) is described based on several female specimens. The two genera Andrassya and Malakhovia are placed in a new family, Andrassyidae fam. n., characterised by presence of six setae in the cephalic sensilla pattern, pocket-like amphids, slender pharynx with posterior widening, paired outstretched ovaries, acute tail without evidence of caudal glands or spinneret. Malakhovia gen. n. differs from Andrassyia mainly in having a small buccal capsule and oviparity. Morphological traits and relationships of the two genera are discussed. The family Andrassyidae is tentatively placed in the order Enoplida.