  We show that next-leading logarithmic (NLL) Balitsky-Fadin-Kuraev-Lipatov
(BFKL) effects can be tested by the forward-jet cross sections recently
measured at HERA. For d\sigma/dx, the NLL corrections are small which confirms
the stability of the BFKL description. The triple differential cross section
d\sigma/dxdk_T^2dQ^2 is sensitive to NLL effects and opens the way for an
experimental test of the full BFKL theoretical framework at NLL accuracy.
