Within a 200pc sphere around the Sun, we search for the Hyades tidal tails in the Gaia DR2 dataset. We used a modified convergent-point method to search for stars with space velocities close to the space velocity of the Hyades cluster. We find a clear indication for the existence of the Hyades tidal tails, a leading tail extending up to 170pc from the centre of the Hyades with 292 stars (36 contaminants), and a trailing tail up to 70pc with 237 stars (32 contaminants). A comparison with an N-body model of the cluster and its tails shows remarkably good coincidence. Five white dwarfs are found in the tails.