I
verb
BAD : I am interested in the way people act towards each other.
GOOD : I am interested in the way people behave towards each other.
BAD : It is time that human beings learned how to act properly, without killing each other.
GOOD : It is time that human beings learned how to behave properly, without killing each other.
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When you are talking about what someone does on a particular occasion, act and behave are interchangeable: 'Passengers who left the flight in Rhodes said that they had seen two men acting/behaving very suspiciously.'
When you are talking generally about what someone does or what people do, use behave: 'You can't expect all babies to behave the same.' 'From the way he behaves, anyone would think that he doesn't get paid.'
II
noun
BAD : He refused to accept responsibility for his acts.
GOOD : He refused to accept responsibility for his actions.
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The noun act is usually used when you want to comment on a particular thing that someone has done: 'It was an act of great courage.' 'These cowardly terrorist acts bring death and suffering to the innocent.'
See also ACTION 2 (↑ action )