The Company was first traded on the Copenhagen Stock Exchange under the new name A.P. Møller - Mærsk A/S on 13 June 2003.
The two former companies A/S Dampskibsselskabet Svendborg and Dampskibsselskabet af 1912, A/S were officially listed on Copenhagen Stock Exchange in 1982 following many years of trading on Over-The-Counter Exchange on the Copenhagen Stock Exchange.

The share capital is DKK 4,395.6 mill. divided equally between DKK 2,197.8 mill. A-capital and DKK 2,197.8 mill. B-capital. Each class consists of shares of DKK 1,000 each. (A number of DKK 500 have also been issued).

A-shares have voting rights and B-shares have none. The B-shares often trade at a premium to the A-shares reflecting higher market liquidity of B-shares than A-shares.

In 1998, both A/S Dampskibsselskabet Svendborg and Dampskibsselskabet af 1912, A/S issued four new shares for each share.
In 2003, A/S A/S Dampskibsselskabet Svendborg issued two new shares for each share and Dampskibsselskabet af 1912, A/S issued one new share for each share.