Ab initio self-consistent-field (SCF), two-configuration SCF (TCSCF), and density functional theory (DFT) calculations on the charge-transfer complexes of doubly Li/Cl-doped oligothiophenes and oligo(p-phenyls) and on respective charged systems without counterions have been carried out in order to study polaron to bipolaron transitions. Oligomer chains up to octamers and the ring structures cyclo-dodecathiophene and cyclo-dodeca(p-phenyl) have been investigated. Special attention is paid to the open-shell biradical character of two isolated polaronic defects. It is found that the TCSCF and the spin-unrestricted DFT methods can be successfully applied. A bipolaron structure is obtained when the doping atoms are located on neighboring rings and when there is one undoped ring separating the two doped ones. If there are two or more undoped rings in between a two-polaron configuration (biradical) is found. The bipolaron system is calculated to be more stable than the two-polaron case when counterions are taken into account. The stabilities are reversed if the bare doubly-charged systems are considered. A theoretical estimate for the barrier height of the polaron to bipolaron transition is given using model reaction coordinates.