  We give an explicit bound for the $L_1$-distance between two additive
processes of local characteristics $(f_j(\cdot),\sigma^2(\cdot),\nu_j)$, $j =
1,2$. The cases $\sigma =0$ and $\sigma > 0$ are both treated. We allow $\nu_1$
and $\nu_2$ to be equivalent time-homogeneous L\'evy measures, possibly with
infinite variation. Some examples of possible applications are discussed.
