The 2012 case concerned Cheryl Perich, who had been a teacher at a Lutheran school in Michigan. Ms. Perich said she was fired for pursuing an employment discrimination claim based on a disability, narcolepsy.

Ms. Perich was a “called” teacher who had completed religious training and whom the school considered a minister. The Supreme Court ruled that she was subject to the exception and could not sue.

The new cases concern teachers without formal training or titles but who taught Catholic doctrine and other subjects. One of them, Kristen Biel, sued under the Americans With Disabilities Act after she was diagnosed with breast cancer and her contract was not renewed. The other, Agnes Morrissey-Berru, sued for age discrimination after her own contract was not renewed.

Federal trial judges dismissed both cases, saying the ministerial exception protected the schools. But the United States Court of Appeals for the Ninth Circuit, in San Francisco, reversed those rulings, allowing the cases to proceed.

In separate decisions, the appeals court said the teachers were not covered by the exception established by the 2012 decision because neither they were not considered ministers by either themselves or their employers, as reflected in their job titles.

“Morrissey-Berru’s formal title of ‘teacher’ was secular,” a three-judge panel of the Ninth Circuit wrote in an unsigned opinion. “Aside from taking a single course on the history of the Catholic church, Morrissey-Berru did not have any religious credential, training or ministerial background. Morrissey-Berru also did not hold herself out to the public as a religious leader or minister.”

“She committed to incorporate Catholic values and teachings into her curriculum, as evidenced by several of the employment agreements she signed, led her students in daily prayer, was in charge of liturgy planning for a monthly Mass, and directed and produced a performance by her students during the school’s Easter celebration every year,” the opinion said. “However, an employee’s duties alone are not dispositive.”