A device for the fluid-conveying connection of at least one application probe. The device comprising at least two coaxially extending application line elements, with a supply tubing set, said tubing set comprising at least two parallel-extending supply line elements, in a grip element of a surgical instrument such as a cryosurgical instrument, such that, in a connected state, each supply line element is in fluid communication with at least one associated application line element. A fluid-diverting element is provided and arranged, or can be arranged, in the grip element in fluid communication with an application line connecting region for the connection of the application line elements and with a supply line connecting region for the connection of the supply line elements. At least two transfer line elements designed as an integral part of the fluid-diverting element are in fluid communication with the application line connecting region via the application line connecting region.