Preliminary results are presented of the first (searching) stage of our observational program of the search and study of weak blue star-like objects in the two small γ-ray burst boxes GB 790418 and GB 790613. The basic search purposes are (1) the selection of star-like objects weaker than 23m inside these boxes, (2) the selection of the bluest ones in B — V among these objects. The first result is the fact that there are no blue (with B — V < 0) star-like objects brighter than 24m in both boxes. But in each of these GRB error boxes one blue object with smaller flux was selected for further study to elucidate their nature. In the smallest of the archival GRB error boxes (GB 790613) obtained by three satellite triangulation, the bluest star-like object with V = 24.56(±0.16) and B — V = −0.20(±0.19) is near the center (at the distance < 10") of the GRB box. In the GB 790418 error box, the bluest star-like object with B = 24.40(±0.20), B — V = −0.40(±0.40) is found at ≈50" from the center.