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Let $\cal C$ be a set of curves in the plane such that no three curves in$\cal C$ intersect at a single point and every pair of curves in $\cal C$intersect at exactly one point which is either a crossing or a touching point.According to a conjecture of J\'anos Pach the number of pairs of curves in$\cal C$ that touch each other is $O(|{\cal C}|)$. We prove this conjecture for$x$-monotone curves.

On the number of tangencies among 1-intersecting curves