We study unparticle effects on particle and antiparticle osillations in meson-antimeson, and muonium-antimuonium systems. Unlike usual tree level contributions to meson oscillations from heavy particle exchange with small $Gamma_{12}$, the unparticle may have sizeable contributions to both $M_{12}$ and $Gamma_{12}$ due to fractional dimension $d_U$ of the unparticle. We find that very stringent constraints on the unparticle and particle interactions can be obtained. If unparticle effect dominates the contributions (which may happen in $D^0-bar D^0$ mixing) to meson mixing parameters $x$ and $y$, we find that $x/y =cot(pi d_U)$. Interesting constraints on unparticle and particle interactions can also be obtained using muonion and antimuonion oscillation data. We also comment on unparticle effects on CP violation in meson oscillations.
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