  We investigate the description of excitonic effects within time-dependent
density-functional theory (TDDFT). The exchange-correlation kernel f_xc
introduced in TDDFT allows a clear separation of quasiparticle and excitonic
effects. Using a diagrammatic representation for f_xc, we express its excitonic
part f_xc^Ex in terms of the effective vertex function Lambda. The latter
fulfills an integral equation which thereby establishes the exact
correspondence between TDDFT and the standard many-body approach based on
Bethe-Salpeter equation (BSE).The diagrammatic structure of the kernel in the
equation for Lambda suggests the possibility of strong cancellation effects.
Should the cancellation take place, already the first-order approximation to
f_xc^Ex is sufficient. A potential advantage of TDDFT over the many-body BSE
method is thus dependent on the efficiency of the above-quoted cancellation. We
explicitly verify this for an analytically solvable two-dimensional two-band
model. The calculations confirm that the low-order f_xc^Ex perfectly describes
the bound exciton as well as the excitonic effects in the continuous spectrum
in a wide range of the electron--hole coupling strength.
