In 1845 he travelled to Morocco and Algiers, and in 1847 embarked on a longer African journey, accompanied by Alfred Brehm as his secretary.
Müller left Brehm there and returned to Germany with the natural history specimens collected on his journey, and made plans for a third expedition.
Unfortunately Müller ran into financial difficulties and was not able to rejoin Brehm, instead sending him funds to proceed to Khartoum with Alfred's brother Oskar and a doctor called Richard Vierthaler.
He also began work on an illustrated book entitled Beiträge zur Ornithologie Afrikas (1853-1870), of which only five parts were ever published.
He then travelled to North America, and on his return wrote Reisen in den Vereinigten Staaten, Canada, und Mexiko (1864-1865).