Is it illegal for someone to steal my songs?

ok. i'm a singer, and a songwriter and i wanna be discovered. this question is NOT me asking for ways to get discovered (though i guess suggestions arent unwelcome), this is a question of something else. i've been considerin takin videos of me singing my songs, and puttin them on youtube in the hopes of gettin discovered like some others, but i'm worried that someone will steal my songs and claim them as their own. is this legal? and if it isn't, wat would i be able to do if it happened? please help me figure this out....