In this survey we present in a condensed exposition good approximation
s of probability densities of LS estimators in nonlinear regression mo
dels. This includes also marginal densities or densities of scalar par
ametric functions. Further, the main ideas of two approaches how to us
e these densities for optimal experimental design are presented: the a
pproach using the second order approximation technique, and the approa
ch using optimality criteria in an integral form.