There are multiple artists with this name:

1. The story began in Japan in 1966 when 5 highschool boys started the band influenced by the Ventures. They were Mikiharu Suzuki (drums), Tarou Miyuki (guitarr), Hiromitu Suzuki (Vocals), Kaoru Murakami (Bas)and Masaru Hoshi (lead Gtr,Vocals).
In November 1967 The Mops (モップス) debuted as the "The First Psychedelic band in Japan" and they released their first single "Asamade Matenai". In April 1968 they released their first album called "Psychedelic Sound In Japan". It contains both covers and their own songs.
In 1969 bassist Murakami quit the band, and Miyuki switched to bass from guitar. At this time psychadelic music died out and the Mops switched to playing hard rock. They released 13 singles and 8 albums until they disbanded in May 1974.

2. The Mops was a short-lived punk and power pop influenced rock band from Sweden. Between 1982 and 1983, they released three singles through the label Trend.
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Artist biography from last.fm