The two filed their nomination papers for the July 3 by-poll slated in the presence of Chief Minister Naveen Patnaik, senior BJD leaders including Parliamentary Affairs Minister Bikram Arukh.
The by-elections were necessitated following the election of party leaders Sashi Bhushan Behera and Rabinarayan Mohapatra to the Assembly in the recent elections. The two seats fell vacant after they gave up their Rajya Sabha membership.
While Singhdeo filed his nomination for the seat vacated by Mohapatra, which has nearly four years of its term left, Singh filed his papers for the seat vacated by Behera with about two years of its tenure left, assembly officials said.
On June 12, BJD candidate and Odia film actor Anubhab Mohanty was elected unopposed to the Upper House of Parliament as no one filed nomination for the seat.