The geometry of the k-osculator bundle $(Osc^kM,\pi,M)$ has been studied by R. Miron and Gh. Atanasiu in their joint papers [5-7]. Obviously, the osculator bundle of second order, or the bundle of accelerations correspond to the case $k=2$, [1, 5], and $Osc^1M$ is the tangent bundle $\mathrm{TM}$ of the base manifold $\mathrm M$ [4]. In the present paper we consider the group $G_{ac}$ of transformations of almost complex $\mathrm N$-linear connections on $Osc^2M$ and we determine its invariants, which are $d$-tensor fields. By means of these invariants, we get characterizations of the integrability of type I, II, III or IV for the almost complex $d$-structures on $Osc^2M$. All this integrability relies only on the geometry of 2-osculator bundle $(Osc^2M,\pi,M)$.