The effects of kinetic plus-minus asymmetry and formation of inactive double strands on the self-replication of single-stranded RNA were investigated by analytical and computer simulation methods. It was found that extensions of the analysis developed previously for more restricted models lead to simple formulations that can be used for interpretation of experiments. Relaxation to linear growth or to steady-state conditions for double-strand formation was found to depend upon initial conditions but to be essentially complete for typical laboratory situations. Experimental data confirmed that in the linear growth phase the total nucleotide incorporation rate is about equal in the complementary strands; mostly double strand is formed. However, the enzyme is usually not shared equally, and some steps proceed at different rates in the two strands. The asymmetry is, however, not found to be dramatic for any of the RNA variants studied so far. It appears that the observed prevalence of kinetically rather symmetric self-replication is due to selection of RNA species with similar rate constants during the exponential growth phase.