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The purpose of this paper is to study almost cosymplectic p-spheres and almost cosym-plectic metric bi-structures.Firstly,we show some properties of almost cosymplectic p-spheres.Then we introduce the notion of almost cosymplectic metric bi-structures and give some results on three dimensional manifolds admitting almost cosymplectic metric bi-structures.Moreover,we investigate three dimensional manifolds with almost cosymplectic metric bi-structures when the(1,1)-type tensor fields h1 and h2 are being of codazzi type and cyclic parallel.