An enormous amount of publications deals with smoothing in the sense of nonpara-

metric regression. However, nearly all of the literature treats the case where predictors

and response are related in the form of a function y = m(x) + noise. In many situa-

tions this simple functional model does not capture adequately the essential relation

between predictor and response. We show by means of speed-°ow diagrams, that

a more general setting may be required, allowing for multifunctions instead of only

functions. It turns out that in this case the conditional modes are more appropriate

for the estimation of the underlying relation than the commonly used mean or the

median. Estimation is achieved using a conditional mean-shift procedure, which is

adapted to the present situation.