The pair had been bitching with one another over the social networking site when Zayn raised the stakes by tweeting to Max: "Alright chlamydia boy ;)."
The insult apparently followed a social meeting between Zayn's GF Perrie Edwards (of Little Mix) and Max's ex-GF, Coronation Street star Michelle Keegan.
Both stars have now deleted the majority of their row, but The Mirror reports that it appeared to stem from Zayn repeatedly calling Max a "geek".
Max had tweeted a picture of himself with Gangnam Style star Psy, to which Zayn responded: "The first step is acceptance #geekoftheweek."
Max tried to play along by replying: "Does that mean I'm 'in'."
But Zayn appeared to lose his rag, writing: "I'm not sure why your still talking to me mate conversation ended when I called you a geek. p.s your display just how's how much of a wannabe you are :)"
The exact sequence of tweets is unclear, but apparently Max told Zayn to "Grow up son" - and to "Stay off the bud... It clearly makes u cranky."
The Wanted's Tom Parker and 1D's Louis Tomlinson also got involved in the online handbags, which ended with Max trying to smooth things over but Zayn still stroppy.
Max wrote: "No dramas peeps its all just flirting! Haha."
To which Zayn replied: "Clearly some people are not very familiar with flirting :)."
And his final message is about the only trace of the drama still remaining on his Twitter feed.
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