This thesis describes approaches to bicyclic nitrogen heterocycles, similar to those found in the natural products castanospermine and australine, using a ring-closing metathesis reaction as the key step. These polyhydroxylated natural products, the indolizidine and pyrrolizidine alkaloids are becoming increasingly popular in both chemical and biological syntheses, due to their antiviral and anti-cancer properties. Numerous syntheses have been attempted to try and produce polyhydroxylated alkaloids with a short synthetic sequence and a ring closing metathesis reaction as the key step. The ring closing metathesis reaction produces a fused bicyclic system containing a cis alkene, which can then be functionalised to form the polyhydroxylated structure similar to the type of natural products described. The most successful synthesis uses a double ring-closing metathesis reaction as the key step, forming two alkenes in the final fused ring system. By varying the starting materials used it is possible to produce different size bicyclic rings.