People’s Artist of the Soviet Union, National Prize Winner, he studied in the Leningrad Choral School named after Glinka. Dmitriev continued his music education at the Leningrad Conservatoire, where he studied choir conducting under the tutelage of E. Kudriavtseva, and learned choral theory from Y. Tiulin. Then he enrolled in a graduate course in Symphonic Conducting, taught by Nikolai Rabinovich. In 2006 he won the 2nd National Conducting Competition.

From 1961 to 1971 he was the conductor of the Symphony Orchestra of Karelian Radio and Television. In 1968 through 1969, he took an internship at the Academy of Music and Performing Arts in Vienna, under H. Swarovski and K. Osterreicher, and then - in the Honoured Orchestra under E. Mravinsky.

In 1971 Dmitriev became head conductor of the Leningrad Maly Opera and Ballet Theatre. Since 1977 he has worked as the chief conductor of the Academic Symphony Orchestra of the Philharmonic for 30 years; at the same time he also conducted the Symphony Orchestra of Stavanger, Norway, from 1990 to 1998, and taught the symphony conducting at the Leningrad Conservatory till 1992. Posters of Dmitriev’s concerts demonstrate music of nearly all epoch and styles. The repertoire of Alexander Dmitriev includes works of American and Scandinavian composers, Russian music of XIX–XX centuries, and symphonic classics of the XX century. Dmitriev augmented the orchestra’s discography with all the symphonies of Beethoven and Schubert, and numerous works by Tchaikovsky, Rachmaninov, Ravel and Britten. Dmitreiv’s partnership with his orchestra has been filled with much touring in Russia, Europe, Asia and the Americas.