In this paper a Weil approach to quasijets is discussed. For given manifolds $M$ and $N$, a quasijet with source $x\in M$ and target $y\in N$ is a mapping $T_x^{r}M\to T_y^{r}N$ which is a vector homomorphism for each one of the $r$ vector bundle structures of the iterated tangent bundle $T^r$ [, Casopis Pest. Mat. 111, No. 4, 345-352 (1986; Zbl 0611.58004)]. Let us denote by $Q{J}^r(M,N)$ the bundle of quasijets from $M$ to $N$; the space ${\tilde{J}}^r(M,N)$ of non-holonomic $r$-jets from $M$ to $N$ is embeded into $Q{J}^r(M,N)$. On the other hand, the bundle $Q{T}_m^{r}N$ of $(m,r)$-quasivelocities...