In a process for dyeing a textile web, dye is applied directly to a first face of the textile web other than by saturating the web. The web is moved in an open configuration thereof over a contact surface of an ultrasonic vibration system with a second (opposite) face of the textile web in direct contact with the contact surface of the ultrasonic vibration system and the first face free from contact with the contact surface of the ultrasonic vibration system. The ultrasonic vibration system is operated to impart ultrasonic energy to the second face of the textile web to facilitate movement of the dye from the first face of the web into and through the web to the second face thereof. In another embodiment, dye is applied to the first face of the textile web without applying the dye to the second face of the web.