Big M is one of five other brands Marshall produced in the 1960s (CMI, Park, Kitchen Marshall, and Narb were the other four). As Marshall grew as a compnay, they began selling amplifiers in different countries, including Germany. However, a German company was already using the name Marshall on a line of trumpets, and Jim Marshall wasn't able to use the brand on his amplifiers. In 1966, he started building amps for Germany under the name "Big M" that were simply Marshall amplifiers with a different name on the front. The Big M trademark was relatively short-lived since by 1968, Jim bought the rights to Marshall trumpets in Germany and stopped producing Big M amplifiers since he could now sell Marshall amplifiers there.
Big M reappeared in 1975, in the American market. Marshall/Rose-Morris marketing executives decided that building amps in America would be cheaper, and thus boost sales so the second run of Big M amplifiers were manufactured in Long Island, NY. The new Big M built both solid-state and tube heads, for lead and bass applications. They also made some speaker cabinets with some new features, such as the extended frequency enclosure. These units were cheaper and used Eminence speakers, instead of Celestions. The second run of Big M lasted less than a year and they were discontinued. Big M never made a third comeback. Source: Michael Doyle, The History of Marshall.
Amplifiers previously produced in England by Marshall between 1966 and 1968, and in Long Island, NY in 1975.