Alex speaks truth only once a day in a week. Below are a few hints for you:

First: Days are Sunday, Monday and so on.

Second: One day he says, "I lie on Monday and Tuesday".

Third: On the next day, he says, "Today is either Thursday, Saturday or Sunday".

Fourth: On the next day, he says, "I lie on Wednesday and Friday".

Can you identify the day on which he speaks truth?

Alex speaks truth on Thursday.