A method for laying and/or recovering a flexible line in a body of water, comprising: - provision of a laying device comprising a pair of upper tensioners and a pair of lower tensioners, each pair of tensioners (72A; 72B) defining a passage for circulation of the line in which the line is locally clamped; each tensioner (72A; 72B) comprising a member for moving the line and at least one motor for setting the movement member in motion, operable to deliver a torque for moving the line; - a control unit for each motor, the method comprising: at least one laying and/or recovery phase in which the control unit activates the motor of at least one tensioner (72A; 72B) and delivers a movement torque generating a continuous movement of the line through each circulation passage; - at least one phase of near-immobilization or immobilization of the line; characterized in that the or each phase of near-immobilization or immobilization of the line comprises the following steps: - activating the motor of at least one upper tensioner and/or at least one lower tensioner by the control unit, in order to apply to the movement member of the upper tensioner and/or of the lower tensioner a torque for holding the line against its weight by the pair of upper tensioners and/or by the pair of lower tensioners, - at least occasional control by the control unit of at least one motor of an upper tensioner and/or of a lower tensioner for causing a movement member of the upper tensioner and/or the lower tensioner to move or for changing the holding torque applied to the movement member of the upper tensioner and/or of the lower tensioner without moving the movement member of the upper tensioner and/or lower tensioner. - provision of a laying device comprising a pair of upper tensioners and a pair of lower tensioners, each pair of tensioners (72A; 72B) defining a passage for circulation of the line in which the line is locally clamped; each tensioner (72A; 72B) comprising a member for moving the line and at least one motor for setting the movement member in motion, operable to deliver a torque for moving the line; - a control unit for each motor, the method comprising: at least one laying and/or recovery phase in which the control unit activates the motor of at least one tensioner (72A; 72B) and delivers a movement torque generating a continuous movement of the line through each circulation passage; - at least one phase of near-immobilization or immobilization of the line; at least one laying and/or recovery phase in which the control unit activates the motor of at least one tensioner (72A; 72B) and delivers a movement torque generating a continuous movement of the line through each circulation passage; - at least one phase of near-immobilization or immobilization of the line; characterized in that the or each phase of near-immobilization or immobilization of the line comprises the following steps: - activating the motor of at least one upper tensioner and/or at least one lower tensioner by the control unit, in order to apply to the movement member of the upper tensioner and/or of the lower tensioner a torque for holding the line against its weight by the pair of upper tensioners and/or by the pair of lower tensioners, - at least occasional control by the control unit of at least one motor of an upper tensioner and/or of a lower tensioner for causing a movement member of the upper tensioner and/or the lower tensioner to move or for changing the holding torque applied to the movement member of the upper tensioner and/or of the lower tensioner without moving the movement member of the upper tensioner and/or lower tensioner. - activating the motor of at least one upper tensioner and/or at least one lower tensioner by the control unit, in order to apply to the movement member of the upper tensioner and/or of the lower tensioner a torque for holding the line against its weight by the pair of upper tensioners and/or by the pair of lower tensioners, - at least occasional control by the control unit of at least one motor of an upper tensioner and/or of a lower tensioner for causing a movement member of the upper tensioner and/or the lower tensioner to move or for changing the holding torque applied to the movement member of the upper tensioner and/or of the lower tensioner without moving the movement member of the upper tensioner and/or lower tensioner.