A plurality of specialized controllers, each one adapted to control a particular type of data transfer operation, control the flow of data between a system bus and a local bus on a computer adapter card. When the Direct Memory Access (DMA) controller is controlling a DMA operation on the local bus, certain other controllers can break-in to the current DMA operation, temporarily halting the DMA operation until the other controller has completed its data transfer operation. To break-in to a DMA operation, handshaking signals between the DMA controller and the local bus interface circuit are temporarily blocked by blocking signals from a break-in logic circuit. The break-in circuit includes a four-state state machine to block the handshaking signals at the appropriate times, and to signal the interrupting controller to begin its data transfer operation. When breaking-in to a DMA operation in this manner, the operation of the DMA controller is not altered; instead, to the DMA controller, it appears that the local bus interface circuit is merely slow to respond with its acknowledge handshake.