Sigiswald Kuijken was born in 1944 close to Brussels. He studied violin at the conservatories of Bruges and Brussels, completing his studies at the latter institution with Maurice Raskin in 1964. He came into contact with early music at a very young age, together with his brother Wieland. Studying on his own, he gained a thorough knowledge of specific 17th- and 18th-century performance techniques and conventions of interpretation on violin and viola da gamba. This led to the introduction, in 1969, of a more authentic way of playing the violin, whereby the instrument was no longer held under the chin, but lay freely on the shoulder; this was to have a crucial influence on the approach to the violin repertoire and was consequently adopted by many players starting in the early 1970s.
From 1964 to 1972, Sigiswald Kuijken was a member of the Brussels-based Alarius Ensemble (with Wieland Kuijken, Robert Kohnen and Janine Rubinlicht), which performed throughout Europe and in the United States. He subsequently undertook individual chamber music projects with a number of Baroque music specialists, chief among which were his brothers Wieland and Barthold and Robert Kohnen, as well as Gustav Leonhardt, Frans Brüggen, Anner Bylsma and René Jacobs.
In 1972, with the encouragement of Deutsche Harmonia Mundi and Gustav Leonhardt, he founded the Baroque orchestra La Petite Bande, which since then has given innumerable concerts throughout Europe, Australia, South America, China and Japan, and has made many recordings for a number of labels (including Deutsche Harmonia Mundi, Seon, Virgin, Accent, Denon, Hyperion and Challenge.
In 1986 he founded the Kuijken String Quartet (with François Fernandez, Marleen Thiers and Wieland Kuijken), which specialises in the quartets and quintets of the Classical period. Recordings of quartets and quintets by Mozart and Haydn have appeared on Denon and Challenge.
Since 1998 Sigiswald Kuijken occasionally brings together two generations Kuijken (his daughters Veronica and Sara and his brother Wieland) to perform string quartets of later periods (Debussy, Schumann, Beethoven, Schubert) often combined with Lieder by Marie Kuijken, soprano and also daughter of Sigiswald, and Veronica Kuijken, piano. Recordings of the two generations have been made for Arcana and Challenge Records.
In 2004 Sigiswald Kuijken reintroduced in practical performance the violoncello da spalla (shoulder cello) very probably the instrument Bach had in mind when writing his six suites for violoncello solo.
From 1971 to 1996, Sigiswald Kuijken taught Baroque violin at the Koninklijk Conservatorium in The Hague and from 1993 to 2009 at the Koninklijk Muziekconservatorium in Brussels.
For many years he was a guest teacher at institutions such as the Royal College of Music in London, Salamanca University, the Accademia Chigiana in Siena, the Conservatoire of Geneva and the Musikhochschule of Leipzig. Since 1998, Sigiswald Kuijken occasionally conducts “modern” symphonic orchestras in romantic programs ( Beethoven, Schumann, Brahms, Mendelssohn).

Veronica Kuijken (1978) started to play piano at age six and violin at age eight. She went to the Brussels conservatory at the age of 16 in the piano class of Daniel Blumenthal. There she took her master's degree in piano cum laude in June 1999. After two years of violin lessons, and privately tutoring for seven years she continued her studies in London and obtained a master's degree in violin in September 1998 (via the Central Examining Committee of the Flemish Community). She has been studying at the Musikhochschule in Winterthur (Switzerland) since October 1999. In 1997 Veronica was selected as a violinist in the European Gustav Mahler Youth Orchestra, conducted by Iván Fischer, Semyon Bychkov and Pierre Boulez. Alongside her studies, Veronica Kuijken and her sister Marie (soprano and pianist) have performed since 1993 as the 'I Pulcini' duo. Veronica has regularly played with the Kammerorchester Basel since 2000, and holds a part-time position as piano accompanist with the Conservatory of Music in Lausanne and as harpsichord accompanist in the Geneva Conservatory.

Wieland Kuijken (1938) obtained a Higher Certificate in cello at the Royal Conservatory of Brussels in 1959. Taught himself to play viola da gamba and 17th and 18th century performance practice. Performed avantgarde music until the late seventies. He often worked together with his two brothers Barthold and Sigiswald and harpsichordist Robert Kohnen. He is much sought after as a teacher and as a cellist known for his interpretation of Bach's solo suites. He also occasionally works as a conductor.

In 1986 the Kuijken String Quartet was founded by early music specialist Sigiswald Kuijken, with François Fernandez, Marleen Thiers and his brother Wieland Kuijken. The ensemble specializes in the quartets and quintets of the Classical period, and is renowned for its important contribution to authentic playing of stringed instruments, especially in works of Haydn and Mozart. The quartet has made numerous acclaimed recordings and toured Europe and North America.
Since 1998 Sigiswald Kuijken occasionally brings together two generations Kuijken (his daughters Veronica and Sara and his brother Wieland) to perform string quartets of later periods, such as those by Beethoven, Schubert, Schumann and Debussy. This quartet is also known as the Kuijken String Quartet.

Marleen Thiers (1945) studied with Arthur Grumiaux and Maurice Raskin at the Conservatory of Brussels. Just like her husband, Sigiswald Kuijken, she immediately showed a special penchant for period instruments and performance practice. She plays first viola in La Petite Bande and is a cofounder and viola player with the Two Generations Kuijken.

Sara Kuijken (1968) studied viola at the Royal Conservatory of Music in Brussels, where she obtained a 1st prize in 1989 and in 1992 the Higher Certificate magna cum laude. At the Sweelinck Conservatory in Amsterdam she obtained a degree as a performing musician in 1995. Together with seven other musicians, she founded the Oxalys chamber music ensemble, in which she played viola and served as artistic director until 1998. This ensemble released two CDs, with impressionist and with contemporary Russian chamber music. Her father Sigiswald Kuijken gave her some baroque violin instruction in 1994. She is a regular participant in La Petite Bande. Since the academic year 2005-06 she has been assistant instructor of baroque violin at the Royal Conservatory of Music in Brussels.