Though born in the Archangelsk region of Russia in 1952, Alexander Levkovich spent most of his life in Ukraine, immersing himself in musical studies in the western Ukrainian city of Lviv. There he first became familiar with the works of Gyorgy Ligeti, Anton Webern and Alfred Schnittke that were to become among the greatest influences in his music. It was during this time that the maestro Valentin Silvestrov befriended the young composer, becoming both his mentor and a dedicated champion of his music. In 1980, Alexander Levkovich graduated from the Lysenko Academy of Music having earned both a degree in Piano Performance and Composition between 1971 and 1980. In 1983, Mr. Levkovich was invited to become a member of the Creative Composer's League of the former Soviet Union, therein taking his place among the finest creative minds of that country. During this time, leading soloists and orchestras in cities throughout the former Soviet Union, including Kiev, St. Petersburg, Baku, Yerevan and Tbilisi, performed many of his works. A master of many musical genres, he had already to date produced a prolific quantity of works, including three symphonies, six chamber cantatas for baritone and chamber orchestra, as well as two concerti. In 1989, Alexander Levkovich was named Composer of the Year in Ukraine, the highest honour possible to be bestowed upon a composer in that country.

While at the peak of his career, Mr. Levkovich emigrated to Israel, where for three years, his broad exposure perpetuated performances not only in Israel, but also in other countries, namely, in Italy and The United States: in 1991, at the Fifth International Festival of Chamber Music in Camerino, Italy, the composer himself participated as pianist in performances of his Piano Trio "Romantic Music" and Septet along with Philip Hirshhorn, Julian Milkis, Dimitri Yablonsky and others. (Other distinguished musicians taking part in the festival included Martha Argerich, Valeri Afanassiev, Youri Bashmet, Alexander Rabinovich, Dora Schvartsberg and Vadim Sakharov.) Then, in 1992, Mr. Levkovich's Symphony for String Orchestra received rave reviews after a performance with the Brooklyn Philharmonic Orchestra in NYC, in a festival known as "ISRAEL: The next generation".

In that same year, Mr. Levkovich became a resident of Canada, and has remained as such to date. Word of Alexander Levkovich's extraordinary talent traveled quickly. In 1993, conductor Gennady Rozhdestvensky and the Stockholm Philharmonic commissioned a work from the composer. What ensued was the "Elegy of Sorrow" to texts by Vladimir Nabokov and Joseph Brodsky, for solo violin and piano, narrator and chamber orchestra. Shortly thereafter, Mr. Levkovich was once again commissioned to write; this time it was at the request of conductor Jukka-Pekka Saraste and the Toronto Symphony Orchestra. His orchestral work "There is No End to My Sorrow" was performed twice by the TSO at Roy Thompson Hall in Toronto. Tamara Bernstein, Music Critic for the National Post in Toronto, described the work as "quietly noble...with an expert but unostentatious orchestration".

Other highlights of recently performed works include:

The Piano Trio No. 2 "Holocaust", commissioned by "The Rachmaninoff Trio", performed in Toronto in May 2000, the Duo Concerto for violin, piano and fourteen strings performed by the Kiev Camerata at the Organ Hall in Kiev, in September 2000.

The "Lullaby" (from "Holocaust Trio") for clarinet and piano, performed by Julian Milkis and Vadim Sakharov at the Sviatoslav Richter Chamber Music Festival "December Evenings", a highly prestigious music festival in Moscow, in December 2000.

Braziliana No. 1 for clarinet and strings, performed by Julian Milkis and the Ensemble del Arte under the direction of Alexander Brussilovsky, at the Kongregationsaal und Boxenstall Neuberg an der Donau, in Neuberg, Germany, in May 2001, as well as the "Elegy of Sorrow" for violin, piano, narrator and chamber orchestra performed by the Kiev Camerata in May, 2001, in Kiev.

In December, 2001, several of Mr. Levkovich's works were performed in the finest concert halls in Russia, namely: the Tchaikovsky Concert Hall, the Great Hall of the Moscow State Conservatory, and Philharmonic Hall in St. Petersburg, a world premiere performance of his Trio "Revelations", by the following distinguished artists: clarinetist Julian Milkis, cellist Alexander Kniaziev, pianist Valeri Afanassiev and actor Veniamin Smiekhov as narrator.

On January 31, 2005, Mr. Levkovich's work "There is no End for my sorrow", was again performed on The Centarra International Music festival by the Winnipeg Symphony Orchestra and conductor Andrey Boreyko.

Jacques Israelievitch, violin, Michael Israelievitch, percussion, and the Julliard Chamber Orchestra in Julliard, New York performed the World Premier of the Concerto for Violin, Percussion and Chamber Orchestra "Isle of a Beautiful Illusion”. Jacques Israelievitch, Michael Israelievitch and conductor Peter Oundjian with the Toronto Symphony Orchestra performed another Premier of the work in April 5th, 2006.

In 2009 his arangment for viola and strings of Shostakovich's Viola Sonata was performed in Concertgebouw Hall (Amsterdam) by Yuri Bashmet and Moscow Soloists Orchestra.

Since 2006 his compositions have been performed by National Ukrainian Chamber Orchestra 'Kiev - Camerata', conductor Valeri Matukhin.