To obtain an amorphous cycloolefin polymer having high transparency, hot shape stability and a narrow molecular weight distribution, and usable for optical components by copolymerizing specified monomers.

The cycloolefin polymer has a melt viscosity of above 0.25 as measured in decalin at 135°C according to DIN 53728, contains polymer units of at least one cycloolefin and, if desired, polymer units of one or more acyclic olefins, and has at one or both ends an olefinically unsaturated group having at least three carbon atoms. This polymer is obtained by polymerizing at least one cycloolefin, if desired, one or more acyclic olefins in the presence of below about 25 mol.%, based on the total amount of the monomer, olefin having at least three carbon atoms and being other than the acyclic olefin and the cycloolefin and a transition metal catalyst.