Modals in the Reported Speech

Can ->Could

• He can swim
• REPORTED SPEECH: Mike said he could swim

May ->Might

• He may  swim
• REPORTED SPEECH: Mike said he migth swim

Must ->Had

• He must swim
• REPORTED SPEECH: Mike said he had to swim

Needn't * ->Did not need

• He needn't swim
• REPORTED SPEECH: Mike said he didn't need to swim

*needn't is a different way of saying: don't need.

• You needn't worry! I will take care of this = You don't need to worry ...

The following modals do not change: Would, could, might, ought to, needn't have, must have, used to.