Let \(\tau\) be a type of a rational group and let \(\kappa\) be an infinite cardinal. A (torsion-free abelian) group G is called \(\kappa\)-homogeneous of type \(\tau\) if every pure subgroup of G of rank less than \(\kappa\) is a homogeneous completely decomposable group of type \(\tau\). A group G is \(\kappa\)-free if every pure subgroup of G of rank less than \(\kappa\) is free. Main results of the paper are: 1. Every homogeneous group of type \(\tau\) is a tensor product of a rank 1 group of type \(\tau\) with a homogeneous group of type (0,0,...). 2. Every \(\kappa\)-homogeneous group of type \(\tau\) is a tensor product of a \(\kappa\)-free group with a rank 1 group of type \(\tau\).