The phase behaviour of binary mixtures of dimethyl ether with nitrogen, or argon, or krypton, or xenon as the second non-polar component has been investigated at temperatures from T = (270 to 110) K and at pressures up to 200 MPa. The measurements were performed in an optical high-pressure cell, fitted with sapphire windows and a magnetic stirrer. The compositions were determined by on-line gas chromatography. Phase separation was observed according to the synthetic method. The measured p(T) isopleths and the interpolated T(x) isobars are presented and discussed. In the classification of van Konynenburg and Scott, the phase behaviour of (dimethyl ether + nitrogen) and (dimethyl ether + argon) corresponds to type III, (dimethyl ether + krypton) to type II, and (dimethyl ether + xenon) to type I (being close to a type II system). In (dimethyl ether + krypton) a quadruple point (solid + solid + fluid + fluid) occurs at about T = 133 K and p = 70 MPa.