1) Zaydi mouvement appeared in time of rebellion during the Umayyad period.  Zayd was recognized as their Imam but he was killed during a revolt in 740. After his death, many revolts happened and were called Zaydi and many Zaydi states appeared. The condition to be a Imam were not very complex. 

2) Zaydism recognizes as imams those of the Prophet’s house who strove to assert the authority of the imamate, "if necessary through armed struggle."