  We study the CP violation in lepton number violating meson decays $M^{\pm}
\to \ell_1^{\pm} \ell_2^{\pm} M^{' \mp}$, where $M$ and $M^{'}$ are
pseudoscalar mesons, $M=K, D, D_s, B, B_c$ and $M^{'}=\pi, K, D, D_s$, and the
charged leptons are $\ell_1, \ell_2 = e, \mu$. It turns out that the
CP-violating difference $S_{-}(M) \equiv [\Gamma(M^- \to \ell_1^- \ell_2^- M^{'
+})-\Gamma(M^+ \to \ell_1^+ \ell_2^+ M^{' -})]$ can become appreciable when two
intermediate on-shell Majorana neutrinos $N_j$ ($j=1,2$) participate in these
decays. Our calculations show that the asymmetry becomes largest when the
masses of $N_1$ and $N_2$ are almost degenerate, i.e., when the mass difference
$\Delta M_N$ becomes comparable with the (small) decay widths $\Gamma_N$ of
these neutrinos: $\Delta M_N \not\gg \Gamma_N$. We show that in such a case,
the CP ratio ${\cal A}_{CP}(M) \equiv [\Gamma(M^- \to \ell_1^- \ell_2^- M^{'
+})-\Gamma(M^+ \to \ell_1^+ \ell_2^+ M^{' -})]/[\Gamma(M^- \to \ell_1^-
\ell_2^- M^{' +})+\Gamma(M^+ \to \ell_1^+ \ell_2^+ M^{' -})]$ becomes a
quantity $\sim 1$. The observation of CP violation in these decays would be
consistent with the existence of the well-motivated $\nu$MSM model with two
almost degenerate heavy neutrinos in the mass range between $M_N \sim
0.1$-$10^1$ GeV.
