Searches for lepton flavor and lepton number violating decays
have been performed at the NA62 experiment based on the analysis of the data collected in 2016-2018.
New upper limits have been set on the branching ratio of several decay modes: $K^+\to\pi^+\mu^- e^+$,
$K^+\to\pi^-\mu^+ e^+$,
$K^+\to\pi^-l^+ l^+ (l = e, \mu)$
and $K^+\to\mu^- \nu e^+ e^+$.
A search for the decay
$K^+\to\pi^-\pi^0 e^+ e^+$ was made for the first time.