THE PAST PROGRESSIVE FORMS OF MAY AND MIGHT ARE FORMED BY ADDING HAVE BEEN + THE -ING FORM OF THE MAIN VERB.

–I didn't see them at the hotel. They may have been having dinner.

–The mail didn't arrive on time. The mailman might have been having trouble with his car.

THE PRESENT PROGRESSIVE FORMS OF MAY AND MIGHT ARE FORMED BY ADDING BE + THE -ING FORM OF THE MAIN VERB.

–We may be calling you in the morning.

–They might be visiting the U.S. this time next year.

NOTE: When must means necessity, the past form is had to. When it means probability, the past is must have + past participle.

Examples of The Progressive Forms of May and Might

• I talked to my parents. They may be coming to visit this weekend.
• She didn't answer the telephone. She may have been taking a bath.