Alignment and parallelism are frequently found between objects in high resolution remote sensing images, and can be used to interpret and describe the observed scenes. In this work, we propose new representations of parallelism and alignment as fuzzy spatial relations, which capture the imprecision in the semantics of both relations. We propose two novel definitions of alignment between objects: local and global. In local alignment each object of the group is aligned with its neighbors, while in global alignment every object of the group is aligned to all other members. Both definitions consider each object as a whole and are based on relative position measures. They are robust with respect to segmentation errors. Furthermore, we propose an efficient graph-based method to determine which are the locally and the globally aligned groups of objects from a set of segmented objects. In addition, we propose a fuzzy definition for the parallel relation, which is also based on relative position measures, and is adequate to represent the parallelism between a globally aligned group of objects and another object or group of objects. Illustrative examples on optical satellite images show the description power of these two relations and their combination for image interpretation.