Steady shear flow properties of an extensive family of dendrimers were examined for the first time in medium to high concentration solutions. For this, the first seven generations of ethylenediamine (EDA) core-polyamidoamine (PAMAM) dendrimers, having molecular weights fi om about 500 to almost 60000 in 30 to 75 wt % solutions In ethylenediamine (EDA) were used. It was found that these dendrimer solutions exhibited typical Newtonian flow behavior as manifested by direct proportionality of the sheer stress to the shear rate (i.e., constant viscosity with respect to both shear stress and shear rate) over the entire range of shear stress and shear rate studied. In addition to this, there was no abrupt change in the slope of the shear viscosity vs molecular weight relationship, indicating that these dendrimers do not interpenetrate to form transient quasi-networks of the "entanglament"-type typically found for long-chain linear or randomly branched macromolecules, nor do they engage in "sticking" interactions characteristic for the suspensions of idealized spherical particles. This rheological behavior is without precedence among high molecular weight synthetic polymers, and it is proposed that it is solely driven by the unique dendrimer macromolecular architecture which above a certain critical generation results in globular, nanoscopic spheroids whose outer surfaces close upon themselves and become impenetrable for other dendrimers or large molecules. The shear viscosity vs Volume fraction dependencies showed that these dendrimers are draining to solvent molecules, but to a lesser extent than the corresponding random-coil type linear macromolecules of comparable molecular weights. These findings are consistent with a "dense-shell" model of dendrimer intramolecular morphology which can also explain their ability to encapsulate small molecular weight species in their "soft and spongy" interiors. From a typical Arrhenius-type temperature dependence of these dendrimer solutions viscosities and from the dependencies of their flow activation energy on molecular weight, it seems that the smallest kinetic unit involved in the dendrimer flow is the dendrimer molecule itself. Strong dependence of the dendrimer solution viscosity on concentration and temperature, as well as its independence on repeated loading, indicates substantial dendrimer Flexibility and ability to deform. On the basis of these results and the supporting computer modeling calculations, it is proposed that the Newtonian flow behavior and the lack of an abrupt change of slope in the zero-shear viscosity vs molecular weight relationships represent characteristic "fingerprint" properties for dendrimers in general and that these properties distinguish these unique macromolecules from all other traditional classes of macromolecular architecture. It is also proposed that the critical degree of branching may be used as a defining structural criterion for distinguishing true dendrimers from their low molecular weight simple branched precursors.