An elastic connecting support for arrangement between a combustion engine and an air filter of a handheld work apparatus is disclosed. The connecting support has a first channel for largely fuel-free air and a second channel for a fuel/air mixture. The connecting support is realized as a single piece, and has, on a first side, an engine connecting flange, at which the first and second channel end, for connection to the combustion engine. The first channel has a first peripheral wall and the second channel has a second peripheral wall. The first peripheral wall and the second peripheral wall are arranged at a distance in relation to each other in a longitudinal section of the connecting support. The channels extend from the first side to a second side of the connecting support. On the second side, the first channel and the second channel end at a common connecting flange.