A line is disclosed for producing logs of web material provided with a system for controlling, in real time, one or more parameters of the logs produced by the line and for facilitating any corrective actions. The line includes a rewinder, a feed path for the logs from the rewinder towards at least one station arranged downstream of the rewinder; and a measurement station. The measurement station includes at least a measurement device for measuring at least one parameter of logs randomly selected from the feed path and held in the measurement station, for example a device for measuring the firmness of the logs. The measurement station further includes first transferring members for transferring selected logs from the feed path to the measurement station, and second transferring members for transferring selected logs from the measurement station to the feed path.