A new class of cutting planes (for integar linear programs) recently introduced by V. Chvátal is discussed. It is shown that Gomary's fundamental cuts are special cases of these cuts. A formula for the depth of a cut with respect to the cone is found. For cuts formed from from binding inequalities only, the optimal choice is reduced to a system of non-linear integar programs. It is shown that under special circumstances Chvátal's cuts formed from all inequalities can be replaced by cuts formed from binding inequalities without decreasing the depth. The above results re applied to fundamental cuts.