The present invention relates to a combined hooding apparatus for packaging by means of a plastic sleeve of the type comprising a support frame on which there is provided: a system for forming a hood of heat-shrinkable plastic material obtainable from a tubular material folded in pleated fashion; a system for supplying said hood to a delivery point arranged at the top of said support frame; a device for fitting said hood, apt to pick up the hood from said system for supplying and fit it onto a load to be wrapped; and an annular structure which is movable vertically on said frame and on which there is fixed a circle group of burners inside which heating of said heat-shrinkable hood is performed, wherein said annular structure is suspended from a top section of said support frame by means of first raising means and is pivotably mounted on a support bracket displaceable vertically on a column of said support frame by means of second raising means, said annular structure being able to be stowed down by pivoting about an axis of rotation of said support bracket.