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We consider classes of locally X-structures of the form LX = (G I Mal .... , an • G 3A •X such that al .... , an •A ~< G}, where X is a countable set of isomorphism types of finitely generated structures. In LX we study (1) closed structures also known as basically saturated structures which are algebraic analogues of existentially closed structures and (2) saturated structures which are algebraic analogues of existentially universal structures. We do not suppose that LX have the amalgamationdoi:10.1016/0168-0072(87)90064-9 fatcat:o44ffwhcljfldbznh72ktsni2y