The group formation problem of the machine and part is a critical issue in the planning stage of cellular manufacturing systems. The machine-part grouping with alternative process plans means to form machine-part groupings in which a part may be processed not only by a specific process but by many alternative processes. For this problem, this study presents an algorithm based on self organizing neural networks, so called SOM (Self Organizing feature Map). The SOM, a special type of neural networks is an intelligent tool for grouping machines and parts in group formation problem of the machine and part. SOM can learn from complex, multi-dimensional data and transform them into visually decipherable clusters. In the proposed algorithm, output layer in SOM network had been set as one-dimensional structure and the number of output node has been set sufficiently large in order to spread out the input vectors in the order of similarity. In the first stage of the proposed algorithm, SOM has been applied twice to form an initial machine-process group. In the second stage, grouping efficacy is considered to transform the initial machine-process group into a final machine-process group and a final machine-part group. The proposed algorithm was tested on well-known machine-part grouping problems with alternative process plans. The results of this computational study demonstrate the superiority of the proposed algorithm. The proposed algorithm can be easily applied to the group formation problem compared to other meta-heuristic based algorithms. In addition, it can be used to solve large-scale group formation problems.