Main atmospheric parameters characterizing the turbulence were measured at the Paranal ESO Observatory (Chile) with the Generalized Seeing Monitor (GSM) during 19 nights in November–December 1998. The median seeing for this period was , a little worse than average, the spatial coherence outer scale of the wavefront m and the median isoplanatic angle . A very good agreement with seeing values given by ESO DIMM was found. Effects of ground layer turbulence were estimated from measurements of temperature micro–fluctuations at several altitudes. These measurements revealed that the first 21 m above ground account for 12.5% of the total turbulent energy. Comparison between GSM and ESO DIMM values have permitted to highlight a local phenomenon which occurs sometimes at the site in the middle of the night. Statistics of the refractive index structure constant in the surface layer is also studied.