How to find nearest point for each point in current layer using ArcGIS Desktop?

Thanks, but not Near_DIST is 0. Search Radius (optional) is must be different "0".

For exp 1 m (in 1 m diameter cicle along nearest-closest points

1. Use GME available from http://www.spatialecology.com/
2. use the "Point distance tool" from the geoprocessing tools of ArcGIS - for proximity calculations to find the object distance in the same layer. You can specify search radius.

I hope this helps..