  We investigate serial double quantum dot systems with on-site and inter-site
interaction by means of Sch\"onhammer-Gunnarsson projection-operator method.
The ground state is established by the competition between extended Kondo
phases and localized singlet phases in spi$ degrees of freedom. We present and
discuss different phases, as discerned by characteristic correlation functions.
We discuss also how different phases would be seen in linear transport
measurements.
