One stabbing happened just before 5 p.m. at the Red Line station in Hollywood at Western Avenue and Hollywood Boulevard.
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The suspect, described only as a male adult, ran from the scene and the knife was not recovered.
Information about the victim's condition was not immediately known.
Train service was shut down during the initial investigation but later resumed.
The second stabbing was reported just after 8 p.m. at the Red Line's MacArthur Park station. A man was wounded after he was stabbed multiple times in the back of his head while he was riding on the train from the 7th Street station, officials say.
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Information about the suspect was not immediately available.
Police were investigating to see if the two incidents were related.