This follows an ultimatum to doctors to return to work by 8am on Monday.
Department spokesperson Sizwe Kupelo said on Monday the department had identified the two doctors, one in Mthatha and one in Port Elizabeth.
"We have written to the two instigators of the strike advising them that what they are doing is gross misconduct, and calling on them to refrain from that," he said.
He said if doctors had not returned by 8am, the department would take legal action which could include seeking an interdict or even dismissal.
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