Method and apparatus for controlling the delivery of polymer material in a sequential injection molding process. In one embodiment, the method provides: delivering a first shot of a first material simultaneously to a plurality of mold cavities; independently sensing for each cavity a property that is indicative of a volume or flow of material that is delivered to the corresponding cavity during the step of delivering the first shot; independently stopping the step of delivering the first shot to one or more cavities according to a program that uses as a variable a signal indicative of the property sensed for the corresponding cavity during delivery of the first shot; and delivering a second shot of a second material simultaneously to the cavities subsequent to the step of stopping the step of delivering the first shot.