We consider explicit two-layer in time finite-difference schemes intended for the shock capturing calculation of weak solutions of quasilinear hyperbolic systems of conservation laws. The accuracy of these schemes in the areas of smoothness of the calculated weak solution is studied. It is shown that in these regions the errors of the difference solution approximately satisfy the hyperbolic system of differential equations, which have characteristics fields that are the same as the approximated system of conservation laws. This implies that in the shock influence region the convergence rate of the difference solution essentially depends on the accuracy with which the scheme approximates the Hugoniot conditions at the shock front. This explains the decrease in the convergence order of NFC (Nonlinear Flux Correction) schemes in the shock influence regions.