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We point out that in processes involving the parton content of the photon theusual effective photon approximation should be modified. The reason is that theparton content of virtual photons is logarithmically suppressed compared toreal photons. We describe this suppression using several simple, physicallymotivated ans\"atze. Although the parton content of the electron in general nolonger factorizes into an electron flux function and a photon structurefunction, it can still be expressed as a single integral. Numerical examplesare given for the \eplem\ collider TRISTAN as well as the $ep$ collider HERA.Comment: 16 pages and 3 figures (available from DREES@WSICPHEN as topdraw or  PS files); LaTeX with equation.sty; MAD/PH/819, BU 94-0

Virtual photon structure functions and the parton content of the electron