A deflection coil system for a picture tube has a primary deflection coil and an auxiliary deflection coil. The primary and auxiliary deflection coils are each operable to produce a respective magnetic field having a first polarity within a region defined by the coil and an opposite polarity in a second region. Each of the two coils is arranged such that part of the positive polarity field of each coil and all of its opposite polarity field, are in each case coupled to the other coil. This cancels the effects of cross coupling of the primary and auxiliary deflection coils, which are placed in proximity to each other on the same axis, for example on the neck and envelope of a television display tube. At least one of the primary and auxiliary deflection coils may be a saddle shaped deflection coil and has a flat end turn section, substantially defining the opposite polarity area. The primary and auxiliary deflection coils are overlapped on the tube over at least part of this end turn section.