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We develop a model in which cosmic rays, in addition to their initial acceleration by a strong shock, are continuously reaccelerated (e.g., by weak shocks) while propagating through the galaxy. The equations describing this acceleration scheme are solved analytically (approximating ionization losses by a cutoff) and numerically. Solutions for the spectra of primary and secondary cosmic rays are given in a closed analytic form, and they allow a rapid search in parameter space for viable propagation models with distributed reacceleration included. The observed boron-to-carbon ratio can be reproduced by the reacceleration theory over a range of escape parameters, some of them quite different from the standard "leaky box" model. It is also shown that even a very modest amount of reacceleration by strong shocks causes the boron-to carbon ratio to level off at sufficiently high energies, and this effect may be observed in the CRNE data. Several other curiosities in the data may be explained naturally if a modest amount of distributed reacceleration is invoked, including (a) the apparent truncation at low energy in the otherwise exponential pathlength distribution associated with the leaky box model, (b) the sub-iron isotopic anomalies and other effects noted by Silberberg et al., and (c) the discrepancy between the reported 10Be lifetime and the lifetime of cosmic rays in the dense strata of the galactic disk.

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