  We study systems with finite number of states $A_i$ ($i=1,..., n$), which
obey the first order kinetics (master equation) without detailed balance. For
any nonzero complex eigenvalue $\lambda$ we prove the inequality $\frac{|\Im
\lambda |}{|\Re \lambda |} \leq \cot\frac{\pi}{n}$. This bound is sharp and it
becomes an equality for an eigenvalue of a simple irreversible cycle $A_1 \to
A_2 \to... \to A_n \to A_1$ with equal rate constants of all transitions.
Therefore, the simple cycle with the equal rate constants has the slowest decay
of the oscillations among all first order kinetic systems with the same number
of states.
