##### 

Exhibit 8.1

List of material subsidiaries

|                                                                        |  |                                   
|----------------------------------------------------------------------- |  | ----------------------------------
|                                                                       
|Legal Entity                                                            |  | Country of Incorporation          
|                                                                       
|Subsidiaries of ASML Holding
    N.V.:                                  |  |                                   
|ASML Netherlands B.V.                                                   |  | Netherlands (Veldhoven)           
|ASML MaskTools B.V.                                                     |  | Netherlands (Veldhoven)           
|ASML Germany GmbH                                                       |  | Germany (Dresden)                 
|ASML France S.a.r.l.                                                    |  | France (Montbonnot)               
|ASML (UK) Ltd.                                                          |  | UK (Paisley (Scotland))           
|ASML Israel (2001) Ltd.                                                 |  | Israel (Ramat-Gan)                
|ASML Ireland Ltd.                                                       |  | Ireland (Dublin)                  
|ASML Italy S.r.l.                                                       |  | Italy (Avezzano)                  
|ASML Hong Kong Ltd.                                                     |  | Hong Kong SAR                     
|ASML Singapore Pte. Ltd.                                                |  | Singapore                         
|ASML Korea Co. Ltd.                                                     |  | Korea (Kyunggi-Do)                
|ASML Japan Co. Ltd.                                                     |  | Japan (Kawasaki-shi, Kanagawa-Ken)
|ASML Shanghai International Trading
    Co. Ltd.                        |  | China/ Shanghai Free Trade Zone   
|ASML (Tianjin) Co. Ltd.                                                 |  | China (Tianjin)                   
|ASML Taiwan Ltd.                                                        |  | Republic of China (Hsinchu)       
|ASML Equipment Malaysia Sdn. Bhd.                                       |  | Malaysia (Penang)                 
|ASML US, Inc.                                                           |  | US (Delaware)                     
|Botanix, Inc.                                                           |  | US (Delaware)                     
|Subsidiaries of ASML US,
    Inc.:                                     
|ASML Capital US, Inc.                                                   |  | US (Delaware)                     
|ASML MaskTools Inc.                                                     |  | US (Delaware)                     
|Subsidiary of ASML Hong Kong
    Ltd.:                                 
|ASML Macau Commercial Offshore Ltd.                                     |  | Macau                             
|Limited partnership with ASML
    Belgium BVBA as the managing partner:
|ASML Finance Belgium CV                                                 |  | Belgium (Turnhout)                
|