The first petition was filed with the Election Commission by Pheu Thai spokesman Prompong Nopparit and party lawyers.
The petition asks the EC to investigate if Suthep Thaugsuban, leader of the PDRC, and Nitithorn Lamlua, a core member of the NSPTR, are still members of the Democrat Party.
The petition said the PDRC is campaigning to block the election, while the NSPTR is urging candidates to boycott registration scheduled for Dec 23-27.
Both groups have also tried to force the prime minister to resign to derail the elections, even though a royal decree has been issued for the polls, the petition sad, arguing this violated Sections 76 and 152 of the constitution.
If the EC finds that Mr Suthep and Mr Nitithorn are still members of the Democrat Party and are receiving support from it, the EC's political party registrar could order the dissolution of the party, the petition said.
The other petition was filed with the Constitution Court by Singthong Buachum, a lawyer for the Pheu Thai Party.
It asks the court to issue an injunction for Mr Suthep to stop the PDRC rally, and to order the dissolution of the Democrat Party, alleging that some Democrat executve committee members had supported the rally and campaigned to block the elections in breach of Sections 112, 113, 215, 216 and 356 of the Criminal Code.