In the first incident, two groups of students clashed at Jaipuria College in north Kolkata, police said.
Jaipuria College Principal Dr Asok Mukhopadahyay, who left the premises before the clash reportedly took place, later told reporters he heard about the incident which happened late afternoon and will sit with all sides within a fortnight to arrive at a solution.
Eyewitnesses said two students suffered injuries in the clash but this was not corroborated by the college authorities.
Police said a force was sent to the spot and the situation was now under control.
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In the other incident, teachers of Charuchandra College did not attend classes today in protest against prolonged gherao by a section of students on Saturday, one of the teachers said.
This triggered a counter demonstration by some students who demanded that the college lifts ban on entry of ex-students and improve facilities of the students' toilet, a spokesman of the TMCP union said.
College Principal Dr Satrajit Ghosh was not available for comments.