The weak-localization contribution (B ) to the conductivity of a tunnel-coupled double-layer electron system is evaluated and its behaviour in weak magnetic fields B perpendicular or parallel to the layers is examined. In a perpendicular field B , (B ) increases and remains dependent on the tunnelling as long as the magnetic field is smaller than /eD _t , where D is the in-plane diffusion coefficient and _t the interlayer tunnelling time. If _t is smaller than the inelastic scattering time, a parallel magnetic field also leads to a considerable increase of the conductivity starting with a B ² -law and saturating at fields higher than /eZ (D _t )^1/2 , where Z is the interlayer distance. In the limit of coherent tunnelling, when _t is comparable to the elastic scattering time, (B ) differs from that of a single-layer system due to ensuing modifications of the diffusion coefficient. A possibility for probing the weak-localization effect in double-layer systems by means of the dependence of the conductivity on the gate-controlled level splitting is discussed.