We develop the Bohl spectrum for nonautonomous linear
differential equation on a half line, which is a spectral concept that lies
between the Lyapunov and the Sacker–Sell spectrum. We prove that
the Bohl spectrum is given by the union of finitely many intervals, and
we show by means of an explicit example that the Bohl spectrum does
not coincide with the Sacker–Sell spectrum in general even for bounded
systems. We demonstrate for this example that any higher-order nonlinear
perturbation is exponentially stable (which is not evident from the
Sacker–Sell spectrum), but we show that in general this is not true. We
also analyze in detail situations in which the Bohl spectrum is identical
to the Sacker–Sell spectrum.