The disclosure relates to a packaging machine and to a method of forming a vacuum package. A first evacuable chamber is used for accommodating therein a product-accommodating section of a package, whereas a second evacuable chamber is used for accommodating therein an opening section of the package. Pressure gauges measure the pressure in both chambers, and a supply air valve serves to supply air into the first chamber. The disclosure is characterized in that the supply air valve is a control valve and is adapted to be controlled in dependence upon the difference between the pressures which prevail in the first and second chambers and which are measured by means of the two pressure gauges. The disclosure also relates to the fact that a gap is provided in a partition between the two chambers and that an adjuster is provided for varying and adjusting the cross-sectional area of said gap.