On the basis of the best available member list and duplicity information, we have studied the radial structure of Praesepe and of the very young open cluster NGC 6231. We have found mass segregation among the cluster members and between binaries and single stars, which is explained by the greater average mass of the multiple systems. However, the degree of mass segregation for stars between 1.5 and 2.3M_{sun}_ is less pronounced in Praesepe than in the Pleiades. Furthermore, mass segregation is already present in the very young open cluster NGC 6231 although this cluster is likely still not dynamically relaxed. We discuss the implications of these results and propose a qualitative scenario for the evolution of mass segregation in open clusters. In Praesepe the mass function of single stars and primaries appears to be significantly different, like in the Pleiades. We observe an absence of ellipticity of the outer part of Praesepe.