Dette, HolgerMelas, Viatcheslav B.2010-08-032010-08-032010-08-03http://hdl.handle.net/2003/2732210.17877/DE290R-15637The celebrated de la Garza phenomenon states that for a polynomial regression model of degree p-1 any optimal design can be based on at most p design points. In a remarkable paper Yang (2010) showed that this phenomenon exists in many locally optimal design problems for nonlinear models. In the present note we present a different view point on these findings using results about moment theory and Chebyshev systems. In particular, we show that this phenomenon occurs in an even larger class of models than considered so far. AMS subject classification: 62K05enDiscussion Paper / SFB 823;31/2010Chebyshev systemComplete class theoremLocally optimal designMoment spaceSaturated design310330620report