  The validity of the equivalent-photon approximation for two-photon processes
in electron--positron collisions is critically examined. Commonly used forms to
describe hadronic two-photon production are shown to lead to sizeable errors.
An improved two-photon luminosity function is presented, which includes
beyond-leading-logarithmic effects and scalar-photon contributions. Comparisons
of various approximate expressions with the exact calculation in the case of
the total hadronic cross section are given. Furthermore, effects of the poorly
known low-Q2 behaviour of the virtual hadronic cross sections are discussed.
