A method and system for managing a remote control session (RCS) during which control of input mechanisms of authorized users for manipulating a shared computer screen is time-sliced among the authorized users. No more than one authorized user has control of the input mechanisms at each time during the RCS. Each authorized user is able to view the shared portion of the computer screen throughout the RCS and has been assigned a priority, a control time slice (CTS), and an inactivity threshold. Sole control of the input mechanisms is provided to a first authorized user who requested control of the input mechanisms. Sole control of the input mechanisms is transferred from the first authorized user to a second authorized user who requested control of the input mechanisms. The first and second authorized user are each scheduled to have sole control of the input mechanisms for a specified time duration.