Using narrow-band imagery, we have detected a cone of radiation in the [O III]lambda-5007 line in the nuclei of NGC 1365 and 7582 with emission directed, respectively, towards the south-east and south-west. Adopting a distance of 20 Mpc to NGC 1365 and 21 Mpc to NGC 7582, with H0 = 75 km s-1 Mpc-1 the projected dimensions of the cones are about 1.0 x 1.5 and 1.9 x 1.6 kpc, respectively. The presence of these cones had been previously suggested on the basis of images obtained with the TAURUS Fabry-Perot interferometer and spectroscopic observations, and can be clearly seen in our images after the subtraction of the continuum emission. These observations are new examples of cone morphologies of high-excitation gas previously found in other Seyfert 2 galaxies. The analysis of the available data on NGC 1365 and 7582 favours the so-called 'unified AGN models'.