The author proposes a phenomenological model for a possible failure of the Pomeranchuk theorem. This predicts the following relations among asymptotic total cross sections: ${\sigma }_T\left({\pi }^{-}p\right)-{\sigma }_T\left({\pi }^{+}p\right)={\sigma }_T\left(K^{-}n\right)-{\sigma }_T\left(K^{+}n\right)$, ${\sigma }_T\left(K^{+}p\right)={\sigma }_T\left(K^{+}n\right)$, $\frac{2}{3}\left[{\sigma }_T\right(K^{-}n)-{\sigma }_T(K^{+}n\left)\right]\le {\sigma }_T\left(K^{-}p\right)-{\sigma }_T\left(K^{+}p\right)\le 2\left[{\sigma }_T\right(K^{-}n)-{\sigma }_T(K^{+}n\left)\right]$, ${\sigma }_T\mathrm{}\left(\mathrm{pp}\right)={\sigma }_T\mathrm{}\left(\mathrm{pn}\right)\mathrm{}$, and $\frac{2}{3}\left[{\sigma }_T\right(\overline{p}n)-{\sigma }_T\mathrm{}(\mathrm{pn}\left)\right]\le {\sigma }_T\left(\overline{p}p\right)-{\sigma }_T\mathrm{}\left(\mathrm{pp}\right)\mathrm{}\le 2\left[{\sigma }_T\right(\overline{p}n)-{\sigma }_T\mathrm{}(\mathrm{pn}\left)\right]$. All of these are consistent with the recent Serpukhov data.

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