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Health scare for Liev Schreiber ... he's hospitalized in New York City, where he's going through a battery of tests.

Sources with direct knowledge tell TMZ … the "Ray Donovan" star had a massive headache Sunday and he called his doctor, who told him to immediately go to a hospital.

We're told 58-year-old Liev followed his doctor's advice and stayed overnight Sunday at a NYC hospital ... and today, doctors have been running tests on him. Getty

It's unclear what is ailing Liev -- our sources say doctors don't know the nature of the problem -- but we're told Liev is able to speak and walk without any issues and has the full use of his limbs.

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