Usually it's called a Side-Scrolling "Beat'em up" or a Brawler. I don't know any specific games to recommend though.
http://store.steampowered.com/tag/en/Beat%20%27em%20up/#tag%5B%5D=3871&p=0&tab=Discounts
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Try clicking on the tags on the page. You can find games matching those genres. Or just look at the "games like this" section at the bottom of each page.
There's also google and other resources:
https://www.giantbomb.com/double-dragon/3030-20752/similar-games/
http://www.moregameslike.com/double-dragon/
store.steampowered.com/recommended/morelike/app/252350/
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Hello , can you help me to find fighting games like Mother Russia Bleeds , Double Dragon , Streets of Rage - need games like these ones with the same fighting system ... Thanks :)
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