Mass selective axial ejection of ions and mass analysis with a stability island with linear quadrupoles with added octopole fields are described. With mass selective axial ejection, quadrupoles with 2.0% and 2.6% added octopole fields have been tested and compared to a conventional quadrupole. The effects of trapping ions at different q values, excitation voltage, scan direction, balanced and unbalanced rf voltages on the rods, and dc applied between the rods have been investigated. The highest scan speeds and highest resolution are obtained with resonant excitation and ejection at high q (q = 0.8). With axial ejection, the quadrupole with a 2.0% added octopole field provides mass resolution and ejection efficiencies similar to a conventional rod set. Quadrupole, dipole and simultaneous dipole-dipole excitation between the x and y rod pairs were compared and no advantage was found with quadrupole or dipole-dipole excitation. The effects of scan speed were investigated and a resolution at half height of about 1600 is possible at scan speeds up to 5000 Th/s. Mass analysis using islands of stability was investigated with a quadrupole with2.0% added octopole field. The island of stability is formed with auxiliary excitation. The experiments confirm the predictions of the simulations. With the resolving dc applied to the quadrupole so that the Mathieu parameter a>0, conventional mass analysis with applied rf and dc and no auxiliary excitation is possible. In this case use of an island of stability yields similar peak shape and resolution. However with the polarity of the resolving dc reversed so that a<0, only very low resolution can be obtained; the added octopole prevents conventional mass analysis. By using a stability island when a<0, the resolution is substantially improved.