  We calculate the energy spectra of cosmic rays (CR) and their secondaries
produced in a supernova remnant (SNR), taking into account the time-dependence
of the SNR shock. We model the trajectories of charged particles as a random
walk with a prescribed diffusioncoefficient, accelerating the particles at each
shock crossing. Secondary production by CRs colliding with gas is included as a
Monte Carlo process. We find that SNRs produce less antimatter than suggested
previously: The positron/electron ratio and the antiproton/proton ratio are a
few percent and few $\times 10^{-5}$, respectively. Both ratios do not rise
with energy.
