A Frenchman who claims to have invented the yellow smiley face back in 1968 is opposing Wal-Mart's move.
For many, the symbol is a distinct part of rave culture, and for years clubbers wore t-shirts emblazoned with the logo like it was an unofficial uniform.
It has also become a popular tool used on Internet messageboards to convey feelings or a tone of voice.
The smiley face originally popped up as a popular image in 1970s counter-culture, and has since been adopted by a number of different groups.
But since 1996 Wal-Mart has used the image in the US on uniforms, and it wants sole rights to it in the US retail sector.
Franklin Loufrani, the man opposing Wal-Mart, has marketed the sign since the early 1970s and owns rights to the logo in more than 80 countries, excluding the US.
A decision is expected to be made in August 2006.
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