Alexander Puliaev was born in Leningrad (St.Petersburg) He received a piano soloist diploma from the Moscow Conservatory where he studied with Prof. W. A. Natanson. He continued his education in Western Europe, where he took lessons with Gustav Leonhardt, Jos van Immerseel and Ketil Haugsand. He graduated from the Sweelinck Conservatorium in Amsterdam, where his teachers were Anneke Uittenbosch (harpsichord) and Stanley Hoogland (fortepiano). In 1993 he was awarded a prize at the International Harpsichord competition in Warsaw.

Alexander Puliaev lives in Germany, where he is teaching at the Musikhochschule Köln and from where he has continued his international career. He was performing under such conductors as Peter Schreier, Ivor Bolton, Daniel Reuss and Alexandre Rabinovich. He has also performed in chamber ensembles with such artists as Natalia Gutmann, Barbara Schlick, Martha Argerich and Hidemi Suzuki, Dorothee Oberlinger, Anton Steck, Ketil Haugsand as well as with Concerto Köln, Ornamente 99, Kontraste Köln, Ensemble 1700, Das Neue Orchester Köln, Van Wassenaer Orkest and Norwegian Baroque Orchestra.

He has appeared at a wide range of festivals such as Schleswig Holstein Festival, Tage Alter Musik in Herne, Early Music Festival in Boston, Early Music Festival in Utrecht, Festa da Musica in Lissabon, Banchetto Musicale in Vilnius and many others. He has made recordings with BIS and Marc Aurel Edition labels.