Abstract. In thin (Δ< few λ_i) collisionless current sheets in a space plasma like the magnetospheric tail or magnetopause current layer, magnetic fields can grow from thermal fluctuation level by the action of the non-magnetic Weibel instability (Weibel, 1959). The instability is driven by the counter-streaming electron inflow from the "ion diffusion" (ion inertial Hall) region into the inner current (electron inertial) region after thermalisation by the two-stream instability. Under magnetospheric tail conditions it takes ~50 e-folding times (~100 s) for the Weibel field to reach observable amplitudes |b_W|~1 nT. In counter-streaming inflows these fields are of guide field type.