We searched for cross-correlated delays between emissions in optical, near-infrared and gamma-ray bands for 16 blazars detected by Fermi-LAT, using three methods previously discussed in the literature: the interpolation method (Gaskell & Sparke, 1986), the discrete cross-correlation function (Edelson & Krolik, 1988) and the Z-transformed discrete correlation function (Alexander, 1997). Our results confirm the expectation that in all our sample the three NIR bands vary simultaneously. For four objects of our sample (3C 273, Mrk 501, PKS 2155-304, and PMN J0808-0751), no correlation is found between any of the bands available for this study. For the remaining twelve, a correlation was found between the V band and the NIR bands, indicating that in most of them the V band and the NIR bands vary simultaneously. For 3 objects (3C 454.3, PKS 0235+164, and PKS 1510-089) a delayed correlation between the gamma-ray emission and the NIR+V bands was found.