Some users are seeing a few tweets in their timelines that have been marked as favourites by accounts they follow.
Other tweets are showing from accounts that your friends follow.
"Twitter has fundamentally only shown tweets and retweets posted by accounts you personally follow in timelines to date," the Verge reported.
The new experiment by Twitter has left some of its users annoyed, the report added.
According to them, favouriting is inherently a private action.
Many users do not use the favourite in the same way as a Facebook "Like".
Some use it as a simple acknowledgment of receiving a tweet or as a way of saying "thanks".
In a generic blog post on its website, Twitter said it "experiment(s) with features that may never be released to everyone who uses Twitter".
"They help us decide what not to do -- which is important as we work to keep Twitter simple while improving the user experience," it added.