  Our aim is to define and study a structure for some $(4n+3)$-dimensional
manifolds which is named almost coquaternion structure. This structure is
composed of three almost cocomplex structures $(\phi_a, \xi_a, \eta_a)$, $a =
1,2,3$, which satisfy some relations and may be considered as analogous to the
almost quaternion structure for $(4n+4)$-dimensional manifolds.
  The sphere $S^{4n+3}$ is a typical example of differentiable manifold which
admits an almost coquaternion structure $(\phi_a, \xi_a, \eta_a)$, $a = 1,2,3$.
Using the 1-forms $\eta_a$ of the almost coquaternion structure of the sphere
$S^{4n+3}$, C. Teleman defined and studied on $S^{4n+3}$ a nonholonomic
manifold $V^{4n}_{4n+3}$ whose Riemannian metric is the one of a symmetric
space of E. Cartan. Keeping in mind Teleman's idea, we observed that on an
almost coquaternion manifold a nonholonomic (holonomic) manifold of codimension
three can be defined and studied by nonintegrable (completely integrable)
Pfaff's system $\eta_1 = 0$, $\eta_2 = 0$, $\eta_3 = 0$.
