This paper presents new constructions of multistage wave-mixing networks with arbitrary b/spl times/b space-switching elements, where b /spl ges/ 2. In these networks, for a size of F fiber links and W wavelengths per link, converter requirements are O(Flog/sub b/W) or O(FW/b) for rearrangeable nodes, and O(Flog/sub b/Wlog/sub b/(FW)) or O(FWlog/sub b/(FW)/b) for different types of strictly nonblocking nodes inspired from the Cantor topology. In all cases, the worst case number of cascaded conversion is O(log/sub b/W). When b=W /spl les/ F, the required number of converters, and the worst case number of cascaded conversions are respectively O(F) and O(1), and are both optimal up to a constant. The new networks generalize and improve upon previous wave-mixing networks based on 2/spl times/2 space switches.