TECHNOLOGY FOCUS - INSTRUMENTATION AND TESTING - Preferred Components: The pre-membrane unit, the primary membrane unit and the secondary membrane unit are in the form of sheet, disk, tube or hollow fiber. The system for separation of mixtures of gases or liquids, further comprises a compressor to compress a permeate stream from the primary membrane unit to the secondary membrane unit.    TECHNOLOGY FOCUS - POLYMERS - Preferred Process: The polybenzoxazole polymer membrane is prepared from a hydroxy-containing polyimide with pendent hydroxy groups ortho to heterocyclic imide nitrogen. The crosslinked polybenzoxazole polymer membrane is prepared from a polyimide comprising crosslinkable functional groups and pendent hydroxy groups ortho to a heterocyclic imide nitrogen. The primary membrane and the secondary membrane are made from glassy polymer comprising: polysulfones; sulfonated polysulfones; polyetherimides; cellulosic polymers; polyamides; polyimides; polyamide/imides; polyketones, polyether ketones; poly(arylene oxides) including poly(phenylene oxide) and poly(xylene oxide); poly(esteramide-diisocyanate); polyurethanes; polyesters (including polyarylates) including poly(ethylene terephthalate), poly(alkyl methacrylates), poly(acrylates), and poly(phenylene terephthalate); polysulfides; poly(ethylene), poly(propylene), poly(butene-1), poly(4-methyl-1-pentene), polyvinyls, poly(vinyl chloride), poly(vinyl fluoride), poly(vinylidene chloride), poly(vinylidene fluoride), poly(vinyl alcohol), poly(vinyl esters), poly(vinyl pyridines), poly(vinyl pyrrolidones), poly(vinyl ethers), poly(vinyl ketones), poly(vinyl aldehydes), poly(vinyl amides), poly(vinyl amines), poly(vinyl urethanes), poly(vinyl ureas), poly(vinyl phosphates) and poly(vinyl sulfates); polyallyls; poly(benzobenzimidazole); polyhydrazides; polyoxadiazoles; polytriazoles; poly(benzimidazole); polycarbodiimides; polyphosphazines; micro porous polymers; and inter-polymers, and grafts and blends containing any of the polymers. The secondary membrane is made from at least one polybenzoxazole polymer membrane or at least one crosslinked polybenzoxazole polymer membrane. Preferred Components: The first permeate stream comprises waste gases or liquids that are removed from the pre-membrane unit and the first retentate stream comprises product gases or liquids. The first permeate stream comprises a product stream and the first retentate stream comprises waste gases or liquids. The second retentate stream comprises a product stream and the second permeate stream comprises waste gases or liquids. The second retentate stream comprises waste gases or liquids and the second permeate stream comprises product gases and liquids. The third permeate stream comprises a waste stream and the third retentate stream comprises product gases or liquids, which is recycled to pre-membrane unit and/or primary membrane unit. The third permeate stream comprises a product stream and the third retentate stream comprises waste gases or liquids, which is recycled to pre-membrane unit and/or primary membrane unit. The pre-membrane comprises one polybenzoxazole polymer membrane or at least one crosslinked polybenzoxazole polymer membrane. The hydroxy-containing polyimide is formula (I). The polyimide comprising crosslinkable functional groups and pendent hydroxy groups ortho to a heterocyclic imide nitrogen is of formula (II). The secondary membrane unit comprises at least one glassy polymer, preferably polybenzoxazole polymer membrane or crosslinked polybenzoxazole polymer membrane.X1 = oxybis(1,4-phenylene-3-yl), carbonylbis(1,4-phenylene-3-yl), sulfonylbis(1,4-phenylene-3-yl), (perfluoropropane-2,2-diyl)-bis(1,4-phenylene-3-yl), (propane-2,2-diyl)-bis(1,4-phenylene-3-yl), (4,4'-(propane-2,2-diyl)bis(1,4-phenylene))bis(oxy)bis(1,4-phenylene-3-yl), naphthalene-tetrayl, (1,4-phenylenebis(oxy))bis(1,4-phenylene-3-yl), biphenyl-tetrayl, benzene-1,2,4,5-tetrayl, (ethane-1,2-diylbis(oxy))bis(oxomethylene)bis(1,4-phenylene-3-yl) or thiobis(1,4-phenylene-3-yl);X2 = 1,3-dihydroxy-benzene-4,6-diyl, 4,4'-dihydroxy-biphenylene-3,3'-diyl or substituted phenol moiety of formula (III);R = -C(CF3)2-, -C(CH3)2-, -S(=O)2-, -O- and/or -S-;X3 = oxybis(1,4-phenylene-3-yl), carbonylbis(1,4-phenylene-3-yl) or sulfonylbis(1,4-phenylene-3-yl);X4 = (perfluoropropane-2,2-diyl)-bis(1,4-phenylene-3-yl), (propane-2,2-diyl)-bis(1,4-phenylene-3-yl), (4,4'-(propane-2,2-diyl)bis(1,4-phenylene))bis(oxy)bis(1,4-phenylene-3-yl), naphthalene-tetrayl, (1,4-phenylenebis(oxy))bis(1,4-phenylene-3-yl), biphenyl-tetrayl, benzene-1,2,4,5-tetrayl, (ethane-1,2-diylbis(oxy))bis(oxomethylene)bis(1,4-phenylene-3-yl) or thiobis(1,4-phenylene-3-yl); andY1 = 1,3-dihydroxy-benzene-4,6-diyl, 4,4'-dihydroxy-biphenylene-3,3'-diyl or substituted phenol moiety (III). EXAMPLE - No suitable example given.