The production of high-performance composite parts with non-crimp fabrics (NCFs) requires a profound understanding of the material’s behavior during draping to prevent forming defects such as wrinkling and gapping. Simulation methods can be used to model the complex material behavior of NCFs and predict their deformation during the draping process. However, NCFs do not intrinsically deform under pure shear like most woven fabrics, but often under superimposed shear, transverse tension and in-plane roving compaction. Therefore, non-standard characterization methods have to be applied besides typical picture frame tests or bias-extension tests. Off-axis-tension tests (OATs) utilize a simple setup to characterize a fabric’s membrane behavior under different ratios of superimposed shear, transverse tension and in-plane compaction. OATs at three different bias angles (30◦, 45◦ and 60◦) are conducted to investigate a unidirectional and a bidirectional NCF. A method is presented to measure the fiber curvatures in addition to the occurring strains. The investigations reveal a relatively symmetrical, shear-dominated behavior with limited roving slippage for the Biax-NCF. The behavior of the UD-NCF strongly depends on the stitching load during tests and is characterized by an asymmetric shear behavior as well as significant roving slippage. The off-axis-tension test results can be used as the basis for the development and validation of new simulation methods to model the complex membrane behavior of NCFs.