The purpose of this thesis was to characterize the crack growth behaviour in graded materials with directional fatigue crack growth properties. In the titanium alloy Ti-6Al-4V two different microstructural transitions and homogeneous reference specimen for different microstructures were produced by a specific thermomechanical treatment. Using heat treatment in a temperature gradient, a transition from fine lamellar to duplex microstructure and a transition from coarse lamellar to equiaxed microstructure were produced. The transition from fine lamellar to duplex microstructure consists of a homogenous fine lamellar area adjacent to an area of a gradient with increasing volume fraction of primary alpha-phase. The transition of coarse lamellar to equiaxed microstructure forms a defined area with a length of 4 mm between the homogenous microstructures. The existence of two homogenous areas surrounding the microstructural transition makes it possible to determine the crack growth behaviour in the transition area and the influence of the crack path on the crack closure. For this reason, the transition from coarse lamellar to equiaxed microstructure has been used for the fatigue crack growth experiments. The properties of the different microstructural components were characterized in homogeneous reference specimens by hardness measurements and tensile tests and in the transition specimens by the change of hardness and yielding behaviour correlated to the position in the transition area. A procedure for calculating the yielding behaviour of the transition area from the yield curves of the homogeneous microstructures was developed. The comparison of the calculated and the measured yield curves of the transitions shows, that there is no unexpected yielding behaviour in the transition areas. To determine the crack growth behaviour CT-specimens with homogenous reference microstructure and with a transition area in the middle of the specimen (W/2) were produced and cyclic loaded in a servohydraulic testing machine. In the specimen with reference microstructure da/dN-DK curves were measured and fitted in an iterative process with the Paris equation to reduce the scattering. Transition specimens were loaded in two crack growth directions with constant DK and crack growth rate and crack closure were measured directional. By examination of the fracture surfaces with scanning electron microscopy and load reducing experiments using load history effects caused by plasticity induced crack closure, a change in the crack growth mechanism and therefore in the crack closure mechanism from roughness induced crack closure in the lamellar part of the specimen to plasticity induced crack closure in the equiaxed part of the specimen could be proven. It could be shown that even a small fraction of equiaxed microstructure in the transition reduces the roughness induced crack closure of the lamellar microstructure, as well as small fraction of lamellar microstructure raises the plasticity induced crack closure of the equiaxed microstructure. The fatigue behaviour of the microstructural transition shows directionality in the development of the crack closure load with the position in the transition. When the crack grows from coarse lamellar to equiaxed microstructure, Kop in the transition regime is significant higher than in the opposite direction. This leads to directionality in the crack growth rate. The crack grows faster in the direction from equiaxed to coarse lamellar microstructure than in the opposite direction. Iterative removing of the crack path and measuring Kop show, that with the strong decrease in roughness in the transition regime the crack closure load decreases. This indicates that the fraction of lamellar microstructure in the transition affects the crack closure load until a few millimetres behind the crack tip. Analogue to the load history effect a history effect caused by the change in the roughness and therefore by the microstructural transition occurs.