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We consider N-wave type equations related to the orthogonal algebras obtained from the generic ones via additional reductions. The first Z_2-reduction is the canonical one. We impose a second Z_2-reduction and consider also the combined action of both reductions. For all three types of N-wave equations we construct the soliton solutions by appropriately modifying the Zakharov-Shabat dressing method. We also briefly discuss the different types of one-soliton solutions. Especially rich are thedoi:10.3842/sigma.2007.039 fatcat:wds2im2fj5h2hiwlwnxpz6r5hu