  The strong corrections to the R-ratio of electron-positron annihilation into
hadrons are studied at the higher-loop levels. Specifically, the essentials of
continuation of the spacelike perturbative results into the timelike domain are
elucidated. The derivation of a general form of the commonly employed
approximate expression for the R-ratio (which constitutes its truncated
re-expansion at high energies) is delineated, the appearance of the pertinent
$\pi^2$-terms is expounded, and their basic features are examined. It is
demonstrated that the validity range of such approximation is strictly limited
to $\sqrt{s}/\Lambda > \exp(\pi/2) \simeq 4.81$ and that it converges rather
slowly when the energy scale approaches this value. The spectral function
required for the proper calculation of the R-ratio is explicitly derived and
its properties at the higher-loop levels are studied. The developed method of
calculation of the spectral function enables one to obtain the explicit
expression for the latter at an arbitrary loop level. By making use of the
derived spectral function the proper expression for the R-ratio is calculated
up to the five-loop level and its properties are examined. It is shown that the
loop convergence of the proper expression for the R-ratio is better than that
of its commonly employed approximation. The impact of the omitted higher-order
$\pi^2$-terms on the latter is also discussed.
