The only idea of the Khawarij's that could be interpreted favourably by the modern thinkers of today is their theory about the caliphate. They had a quasi-democratic concept of it, and said that the caliph must be chosen by free election, and that the worthiest person was he who had merit as far as faith and piety were concerned. He could be from the Quraysh or not, from a distinguished and famous tribe, or from an insignificant and backward one, Arab or non-Arab.
If, after his election and after everyone had sworn allegiance to him, he took steps in a direction against the interests of the community of Islam, he should be removed from the caliphate, and if he refused, he should be fought with until killed.
In the matter of the caliphate they took a position opposite to that of the Shi`ah, who say that it is a divine office and that the caliph can only be someone who is nominated by God. They were also in opposition to the Sunni, who say the caliphate belongs to the Quraysh and who hold firmly to the principle "innama 'l-a'immatu min qurayshin" - "but the leaders are from the Quraysh:"
Apparently their opinion about the caliphate was not something they had arrived at when they first came into existence. For, according to what their famous slogan "la hukma illa li 'llah" - "no authority except Allah's" -tells us, and also according to what we glean from Nahju 'l balaghah  , they believed, in the beginning, that the people and the society did not need a leader or a government, and that the people should put the Book of God into practice on their own.
However, afterwards, they turned back on this belief and firmly swore allegiance to `Abdullah ibn al-Wahab. 
They recognised the caliphates of Abu Bakr and `Umar to be rightful, because they believed that these two persons had been rightfully elected and that they had not deviated from the way of the best interest, nor perpetrated anything against this best interest. They also recognised the election of `Uthman and `Ali to be rightful; however they said that towards the end of the sixth year of his caliphate, `Uthman changed his direction and ignored the best interest of the Muslims. So he should have been deposed from the caliphate, but since he continued in office he was killed as an unbeliever and his killing was a religious duty. As for 'Ali, since he accepted the arbitration, but did not subsequently repent, he was killed as an unbeliever and his killing was a religious duty. Thus they denounced the caliphate of `Uthman after its seventh year, and that of 'Ali after the arbitration. 
They also abhorred the rest of the caliphs, and were always at war with them.
. See sermon no.40, and also the commentary of Ibn Abi ' l-Hadid, vol.2, p.308
. See Ibn Kathir, al-Kamil fi 't-tarikh.
. See ash-Shahrastani, al-Milal wa 'n-nihal, Cairo, 1961