The two, a university student and a recent graduate, were involved in a play performed at Bangkok's Thammasat University in October 2013 about a fictional monarch and his adviser.
The play, "The Wolf Bride," was performed to mark the anniversary of a successful 1973 anti-dictatorship uprising led by students.
The military-installed administration that took power from an elected government after a coup in May this year has made defending the monarchy a priority in an effort to ensure stability after 87-year-old King Bhumibol Adulyadej ends his reign.
Pawinee Chumsri, the lawyer for Patiwat Saraiyaem and Pornthip Munkong, said they pleaded guilty because they now realize the play had some inappropriate content and they hope a guilty plea will help reduce their sentences, a common practice in criminal cases in Thailand.
Also Read
The Rachada Criminal Court in Bangkok announced that the requests for suspended sentences made by the defendants, who were arrested in August, would be considered and verdicts announced on February 23.
Police last week announced that they could monitor the popular text messaging system Line, an assertion denied by the Japan-based company.
Takorn Tantasith, secretary general of Thailand's National Broadcasting and Telecommunications Commission, said today that he had asked representatives of Internet service providers and social media sites such as Facebook to help monitor and suppress content that might insult the monarchy.
Thai law already allows prosecution of network administrators who do not remove offensive content in a timely fashion, even when posted by third parties.