Abstract : Gamma-ray burst are thought to be produced by highly relativistic outflows. Although upper and lower limits for the outflow initial Lorentz factor γ_0 are available, observational efforts to derive a direct determination of γ_0 have so far failed or provided ambiguous results. As a matter of fact, the shape of the early-time afterglow light curve is strongly sensitive on γ_0 which determines the time of the afterglow peak, i.e. when the outflow and the shocked circumburst material share a comparable amount of energy. We now comment early-time observations of the near-infrared afterglows of GRB 060418 and GRB 060607A performed by the REM robotic telescope. For both events, the afterglow peak was singled out and allowed us to determine the initial fireball Lorentz, γ_0~400.