In a frying apparatus, in particular for grilling, an electric heating device with a contact frying surface is positioned in a mainly box-shaped cabinet with an up-turned opening that may be closed at a distance above the contact frying surface by a preferably transparent cover plate. Structure is provided in connection with the cabinet for conditioning the atmosphere above the contact frying surface at a temperature and air humidity suitable for a specific frying operation, together with an air exhaust for the removal of vapor, fatty particles, smoke and smell from the atmosphere. An air flow of a specific quantity and at controlled temperature and passing substantially horizontally is provided across the contact frying surface towards the air exhaust positioned at one lateral wall of the cabinet, a preferably catalytic filtering device being provided in association with the air exhaust.