In 11 out of 22 individuals, in whom SPAST, ATL1 and REEP1 gene single nucleotide variants (SNV) were previously excluded by Sanger sequencing, we identified three HSP subtypes with AD transmission: WASHC5 (SPG8), KIF5A (SPG10) and KIF1A (SPG30) and SPG11 (SPG11) as the only ARHSPs. This evidence concerns the gene SPAST and Alzheimer disease.