 Two years later in 1984 he released his second, self named, solo album Björn Thoroddsen The following album, Plús (Plus) was released in 1986 and at last the album Quintet.In 1985, Björn formed Gammar, a jazz fusion group, with four other members; Steingrimur Oli Sigurðarson (drums), Stefan S. Stefansson (saxophone), Björn Thoroddsen (guitar), Thorir Baldursson (keyboards) and Skuli Sverrisson (bass).The band released three albums during its time, in 1985 and 1987 the band released two albums Gammar I & II and a few years later, in 1992, they released Af Niðafjöllum (From the Niða mountains

In the end of the last decade Björn met Szymon Kuran a Polish violinist.