A hydraulic transmission apparatus having at least one declutchable hydraulic motor having radial pistons and connected via two motor ducts, and a casing duct connected to the inside of the casing. The apparatus further has clutching means that, in order to perform the clutching of the motor, are suitable for bringing a first one of the motor ducts to a “clutching” first pressure that is higher than the pressure in the casing while also making it possible to remove fluid via the casing duct. Disposed on the casing duct, the apparatus further has means for limiting the flow of fluid in said casing duct, in a manner such as to cause the pressure inside the casing to increase during the clutching operation. This apparatus enables clutching to take place gently.