  For a broad class of nonlinear regression models we investigate the local E-
and c-optimal design problem. It is demonstrated that in many cases the optimal
designs with respect to these optimality criteria are supported at the
Chebyshev points, which are the local extrema of the equi-oscillating best
approximation of the function f_0\equiv 0 by a normalized linear combination of
the regression functions in the corresponding linearized model. The class of
models includes rational, logistic and exponential models and for the rational
regression models the E- and c-optimal design problem is solved explicitly in
many cases.
