Two Janata Dal-United (JD-U) leaders have filed the cases in the Chief Judicial Magistrate's courts in Muzaffarpur and Hajipur districts.
The courts will hear the case on August 1.
The leader who filed the case in Muzaffarpur said Modi not only insulted Nitish but also 11 crore people of Bihar by saying there was some problem with the chief minister's "DNA".
Addressing a public meeting in Muzaffarpur, 70 km from here, Modi on Saturday said: "There seems to be some problem in his DNA because the DNA of democracy is not like that. In a democracy, you give respect even to your political rivals."