Abstract: The invention provides a process for the continuous production of an elongate smoke filtering member comprising a heat-activatable bonding material and having air-permeable deformations at longitudinally displaced positions along its length, which comprises continuously advancing longitudinally a rod-like body of the material of the member, intermittently passing a hot fluid laterally into the advancing body to activate the bonding material substantially only at separate longitudinally displaced regions of the body, and deforming the outer surface of the advancing body at such regions where the bonding material is activated. Apparatus for performing the method comprises means for continuously longitudinally advancing the rod-like body, means for passing a hot fluid laterally into the body at regions longitudinally displaced along the body, and means for deforming the outer surface of the body at said regions.