In this paper, we propose a connected Korean digit recohnition system employing neural networks and lexical constraints of the Korean digits. In the proposed recognition system, firstly, each frame of digit string is labelled by phoneme classification neural networks.which are trained with the reference phoneme segments extracted form an isolated digit based on the position information. And, the frame labels are combined with each other for constructing the phoneme segments. Then, these segments are combined to form a digit candidate using the digit combination rules. The digit candidate is decided based on the condition for digit decision. If the condition is not satisfied, the digit candidate is further recognized using the digit decision neural network in the next step. In our approach, the neural networks are trained with 10 isolated digits uttered by 5 male speakers. To investigate the performance of the proposed recognition system, an intensive computer simulation on the 30 connected digit strings uttered by 5 male speakers is performed. The simulation result indicates that 95.6% digit recognition rate and 82% digit string recognition rate are provided by the proposed Korean digit recognition system.