Wetransformthesingularintegralequationswithsolutionssimultaneouslyhavingsingularitiesofhigherorderatinfinitepointandatseveralfinitepointsontherealaxisintoonesalongaclosedcontourwithsolutionshavingsingularitiesofhigherorder,andfortheformerobtaintheextendedNeothertheoremofcompleteequationaswellasthesolutionsandthesolvableconditionsofcharacteristicequationfromthelatter.Theconclusionsdrawnbythisarticlecontainspecialcasesdiscussedbefore.