They found users suffered heightened anxiety as many felt obligated to keep in constant touch.
Others had trouble disconnecting from social media sites such as Facebook.
The study by scientists Jacob Barkley, Aryn Karpinski and Andrew Lepp is in stark contrast to previous research that found mobile phones improve social interaction and help reduce feelings of isolation.
Previous research has claimed that mobile phones improve social interaction and help reduce feelings of isolation.
But the latest study by Kent University in Ohio found constant phone use was linked to greater stress.
One student said: "The social network sometimes just makes me feel a little bit tied to my phone.
"It makes me feel like I have another obligation in my life."
Another complained that having a mobile phone meant that he could always be contacted at any time.
The researchers used a clinical measure of anxiety and each student's level of satisfaction with their own life in the analysis.
Researcher Andrew Lepp added: "There is no me time or solitude left in some of these students' lives and I think mental health requires a bit of personal alone time to reflect, look inward, process life's events, and just recover from daily stressors."
Those taking part, aged from 18 to 22, allowed the study team to access their exam results, known in the US as a grade point average (GPA), from university records.
"Also, a few of the students we interviewed reported sending texts constantly throughout the day from morning to night that in itself might be stressful."
There are now more mobile phones in the UK than people with the latest figures showing 80.2 million subscription.
The popularity in recent years of smart phones, such as the iPhone, has meant that 94 per cent of all adults own a mobile.