Frederik Muller [1817-1881] began his rare books business in Amsterdam in 1843. In 1876 he was joined by partner and relative Frederick Adama van Scheltema [1846-1899]. After Muller's death, Adama van Scheltema took over the business, negotiating with Muller's heirs over the continued used of the name. In 1885 Anton Mensing [1866-1936] joined the firm, becoming partner in 1892 with Adama van Scheltema. After Schltema's death in 1899, Mensing effectively lead the firm, although it was not until 1905 that the first of several contracts between him and the Muller heirs the allowed him use of the Muller name was finalized.
It was only with Mensing that the firm expanded to include the auction of fine art, although this development was greeted with disfavor by some of the Muller family. In 1901 Mensing hired art historian Fritz Lugt [1884-1970], who was with the firm until the First World War.
In 1929 Mensing's son Ben [Bernhard Franciscus Maria Mensing, 1903-1972] became a partner in the business. Mensing died in 1936 and Ben succeeded him at Frederik Muller & Co., which remained in business until c. 1960. The records of the firm were destroyed after World War II, although a private dossier of the Muller family was acquired by the Print Room of the Rijksmuseum (Inventory no. RP-D-1990:44) when it acquired Frederik Muller's print collection at his death.