Prime Minister Saleh Kebzabo accepted the resignations of defence minister Daoud Yaya Brahim and the government's general secretary Haliki Choua Mahamat, Kebzabo's spokesman said in a statement, without giving further details.
The videos, which were circulated on Sunday and Monday, purportedly showed the men engaging in intimate acts with other people.
Reuters could not independently verify the material and was not immediately able to reach either man for comment.
Sex scandals are rare in Chad, a mostly Muslim country with conservative social mores.
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