PURPOSE: To provide a manufacturing method for bringing the content of an alcohol in a linear polymer obtained by copolymerizing carbon monoxide and at least one olefinically unsaturated compd. in the presence of a lower aliphatic alcohol to below 4,000 wt.ppm, especially, below 100 wt.ppm.

CONSTITUTION: A linear polymer of carbon monoxide and at least one olefinically unsaturated compd., wherein units derived from carbon monoxide and units derived from an olefinically unsaturated compd. are found out in the polymer in substantially alternate order, is produced by bringing monomers into contact with a soln. of a proper catalyst in the presence of a liquid non- polymerizable diluent consisting of at least one or more kind of lower aliphatic alcohol and water at temp. higher than the normal temp. under pressure higher than atmospheric pressure.