Abstract First-order splay faults are secondary faults that form at acute angles to the primary fault when the latter becomes critically misaligned with the direction of maximum principal stress. They are first order in the sense that their slip rate is of the same order as their primary fault. First-order splay faults have been previously described for strike-slip faults and examples are here shown of first-order dip-slip splay faults. For dip-slip faults in sedimentary sequences, friction is often anisotropic, being lower parallel to, rather than oblique to, bedding, and the position of the primary fault is often controlled by a décollement guided by a layer of particularly low friction or a structural feature. In this latter situation, the primary fault may become frictionally misaligned with the direction of maximum principal stress and first-order splay faults may then form. Examples shown are megasplays in subduction zones, ramp faults in fold and thrust belts, and synthetic and antithetic splays of low-angle normal faults.