We introduce ribbon-moves of 2-knots, which are operations to make 2-knots into new 2-knots by local operations in B 4 . (We do not assume the new knots is not equivalent to the old ones.)Let L 1 and L 2 be 2-links. Then the following hold.(1) If L 1 is ribbon-move equivalent to L 2 , then we have.(2) Suppose that L 1 is ribbon-move equivalent to L 2 . Let W i be arbitrary Seifert hypersurfaces for L i . Then the torsion part of H 1 (W 1 ) ⊕ H 1 (W 2 ) is congruent to G ⊕ G for a finite abelian group G.(3) Not all 2-knots are ribbon-move equivalent to the trivial 2-knot.(4) The inverse of (1) is not true.(5) The inverse of (2) is not true. Let L = (L 1 , L 2 ) be a sublink of homology boundary link. Then we have: (i) L is ribbon-move equivalent to a boundary link. (ii) µ(L) = µ(L 1 ) + µ(L 2 ).We would point out the following facts by analogy of the discussions of finite type invariants of 1-knots although they are very easy observations. By the above result (1), we have: the µ-invariant of 2-links is an order zero finite type invariant associated with ribbon-moves and there is a 2-knot whose µ-invariant is not zero. The mod 2 alinking number of (S 2 , T 2 )-links is an order one finite type invariant associated with the ribbon-moves and there is an (S 2 , T 2 )-link whose mod 2 alinking number is not zero.

As analogues of the well-known skein relations for the Alexander and the Jones polynomials for classical links, we present three relations that hold among invariants of high dimensional knots differing by "local moves". Two are for the Alexander polynomials and the other is for the Arf-invariants, the inertia group and the bP-subgroup.

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Let S 3 i be a 3-sphere embedded in the 5-sphere S 5 (i = 1, 2). Let S 3 1 and S 3 2 intersect transversely. Then the intersection C = S 3 1 ∩ S 3 2 is a disjoint collection of circles. Thus we obtain a pair of 1-links, C in S 3 i (i = 1, 2), and a pair of 3-knots, S 3 i in S 5 (i = 1, 2). Conversely let (L 1 , L 2 ) be a pair of 1-links and (X 1 , X 2 ) be a pair of 3-knots. It is natural to ask whether the pair of 1-links (L 1 , L 2 ) is obtained as the intersection of the 3-knots X 1 and X 2 as above. We give a complete answer to this question. Our answer gives a new geometric meaning of the Arf invariant of 1-links.Let f : S 3 −→ S 5 be a smooth transverse immersion. Then the selfintersection C consists of double points. Suppose that C is a single circle in S 5 . Then f −1 (C) in S 3 is a 1-knot or a 2-component 1-link. There is a similar realization problem. We give a complete answer to this question. * 1991 Mathematics Subject Classification. Primary 57M25, 57Q45