[en] The difference between s-wave lengths of πK-scattering asub(0)sup(1/2) - asub(0)sup(3/2)=0.20 msub(π)sup(-1) has been calculated in the superconducting quark model, and the lifetime of the Asub(πK)-dimesonic atom rsub(πK)=6.6x10sup(-15)s has been determined. The main contribution to the difference asup(1/2) - asup(3/2) is shown to be given by q² - terus of box quark diagrams. Thus the origin of this result is interpreted in quite a new way, differing from the known aproaches based on linear or non-linar σ-models. It is noted that the experimental measurement of the Asub(πK) dimesonic atom lifetime allows a direct quantitative checking of q²-expansions of quark loop diagrams employed in the superconducting quark model