1. As it is known, the almost contact metric structure on an odd-dimensional manifold N is de ned by the system of tensor elds f; ; ; gg on this manifold, where  is a vector eld,  is a covector eld,  is a tensor of the type (1; 1) and g = h
;
i is the Riemannian metric [5], [6]. Moreover, the following conditions are ful lled: () = 1; () = 0;    = 0; 2 = ?id +   ; hX;Y i = hX; Y i ?  (X)  (Y ) ; X; Y 2 @(N); where @(N) is the module of the smooth vector elds on N. As examples of almost contact metric structures we can consider the cosymplectic structure, the nearly cosymplectic structure, the Sasaki structure and the Kenmotsu structure. The cosymplectic structure is characterized by the following conditions: r = 0; r = 0; where r is the Levi{Civita connection of the metric. It was proved that the manifold, admitting a cosymplectic structure, is locally equivalent to the product M  R, where M is a Kahlerian manifold [6]. An almost contact metric structure f; ; ; gg is called nearly cosymplectic, if the following condition is ful lled [6], [8]: rX()Y + rY ()X = 0; X; Y 2 @(N): We note that the nearly cosymplectic structures have many remarkable properties and play an important role in contact geometry. We mark out a number of articles by H. Endo on the geometry of nearly cosymplectic manifolds as well as the fundamental research by E.V. Kusova on this subject [8]. It is known that if (N; f; ; ; gg) is an almost contact metric manifold, then an almost Hermitian structure is induced on the product N R [5], [6]. If this almost Hermitian structure is integrable, then the input almost contact metric structure is called normal. A normal contact metric structure is called Sasakian [6]. On the other hand, we can characterize the Sasakian structure by the following condition: rX()Y = hX; Y i  ? (Y )X; X; Y 2 @(N): For example, Sasakian structures are induced on totally umbilical hypersurfaces of Kahlerian manifolds [6], [10]. As it is well known, the Sasakian structures have also many important properties. In 1972 K. Kenmotsu has introduced a class of almost contact metric structures, de ned by the condition rX()Y = hX; Y i  ? (Y )X; X; Y 2 @(N): The Kenmotsu manifolds are normal and integrable, but they are not contact manifolds, consequently, they can not be Sasakian. We mark out that the fundamental monograph by Gh. Pitis [9] contains a detailed description of Kenmotsu manifolds and their generalizations and a set of important results on this subject. 2. Let us consider the rst groups of Cartan structural equations of the most important almost contact metric structures [6], [8], [10]. The rst group of structural equations of the cosymplectic, nearly cosymplectic, Kenmotsu and Sasakian structures are the (1), (2), (3) and (4), respectively: d! = ! ^ ! ; d! = ?! ^ ! ; (1) d! = 0; d! = ! ^ ! + H ! ^ !  + H ! ^ !; d! = ?! ^ ! + H ! ^ !  + H ! ^ !; (2) d! = ? 2 3 G ! ^ ! ? 2 3 G ! ^ ! ; d! = ! ^ ! + ! ^ ! ; d! = ?! ^ ! + ! ^ ! ; (3) d! = 0; d! = ! ^ ! ? i! ^ ! ; d! = ?! ^ ! + i! ^ ! ; (4) d! = ?2i! ^ ! : In [7], V.F. Kirichenko and I.V. Uskorev have introduced a new class of almost contact metric structure. Namely, they have de ned the almost contact metric structure with the close contact form as the structures of cosymplectic type. As they have established, the condition d! = 0 is necessary and sucient for an almost contact metric structure to be of cosymplectic type. V.F. Kirichenko and I.V. Uskorev have also proved that the structure of cosymplectic type is invariant under canonical conformal transformations [7]. We recall also that a conformal transformation of an almost contact metric structure f; ; ; gg on the manifold N is a transition to the almost contact metric structure fe ; e; e; egg, where e = , e = ef , e = e?f  and eg = e?2f g. Here f is a smooth function on the manifold N [6]. Evidently, a trivial example of structure of cosymplectic type is the cosymplectic structure, because it has well-known Cartan structural equations (1). Another important example of the almost contact metric structure of cosymplectic type is the Kenmotsu structure with the Cartan structural equations (3). On the other hand, it is easy to see that the nearly cosymplectic and Sasakian structures are not of cosymplectic type. 3.We consider almost contact metric structures induced on oriented hypersurfaces of six-dimensional sphere with the canonical almost nearly Kahlerian structure [2], [4]. For 2-hypersurfaces (i.e. for hypersurfaces with type number 2) we obtain the following result: Theorem A. The Cartan structural equations of the almost contact metric structure on an oriented 2-hypersurface of the nearly Kahlerian six-sphere are the following: d! = ! ^ ! + B ! ^ !  +  ? p 2 e B3 ? 1 p 2 e B 3 + i  ! ^ !; d! = ?! ^ ! + B ! ^ !  +  ? p 2 e B3 ? 1 p 2 e B 3 ? i  ! ^ !; (5) d! = 0: Here the systems of functions fBabcg and fBabcg are the components of the Kirichenko tensors [1] of the sphere S6 and  is the second fundamental form of the immersion of the 2-hypersurface into S6; a; b; c = 1; : : : ; 6; ; = 1; 2. The structural equations (5) perfectly correspond to the structure of cosymplectic type, but this almost contact metric structure is not cosymplectic or Kenmotsu. So, we have proved the following result. Theorem B. Hypersurfaces with type number two in a nearly Kahlerian six-sphere admit noncosymplectic and non-Kenmotsu almost contact metric structures of cosymplectic type. 4. At the end, we remark that Theorem B generalize the result from [3], where it has been proved that 2-hypersurfaces in an arbitrary Kahlerian manifold also admit non-cosymplectic and nonKenmotsu almost contact metric structures of cosymplectic type. On the other hand, in [2] and [4], it was proved that almost contact metric structure induced on an oriented 0- or 1-hypersurface of the nearly Kahlerian six-sphere S6 is necessarily nearly cosymplectic, i.e. it is not of cosymplectic type.