As the two spheres are brought into contact, the charge on the charged sphere is distributed equally between the two spheres. Now they both have the same charge. Because they have the same charge they are going to repel each other. The two spheres are going to experience repulsion.
Since the conducting spheres are identical, the charge is transferred from the charged sphere to the neutral sphere in such a way that they are now equally charged. The two spheres would experience a force of repulsion, because they are like-charged.