Alexander Geluk studied orchestral conducting with Taijiro Iimori and cello with Robert Dispa at the conservatories of Arnhem and Enschede where he graduated as a cellist and conductor.
His subsequent career was filled by conducting symphony orchestras and choirs and he also composed various symphonic and choral pieces.

At present Alexander holds positions as principal conductor with:
Eastgelders Symphony Orchestra, Arnhem Oratoriochoir, Van Wassenaer Consort and Symfonia Jong Twente. With Symfonia he won the 1st  prize 'with excellence' in the Viennese  'Summa Cum Laude' competition of 2010 and conducted at the winnersconcert in the prestigious 'Wiener Musikverein'. Geluk is also engaged as a guest conductor with - among others - the Beethoven Academy Orchestra (Krakow), He has, among others,  worked  as a  conductor with the Oostnederlands Kamer Orkest, Oostnederlands Symfonie Orkest, Deventer Student Orchestra, Euregio Jugend Symphonie Orchester, Twents Symfonie Orkest, Il Concerto Barocco, Kammersinfonieorchester Darmstadt, Bachkoor Apeldoorn, Continuo Rotterdam , Gelders Begeleidings Orkest , Accompagnato Enschede, Royal Symphony Orchestra 'Cecilia', New Chamber Philharmony of Europe, University Orchestra Enschede , Opera Jong Twente , Orchestra and Choir of the Saxion University, Pro Musica Münster , Jeugd Orkest Nederland , Neue Ruhr Kammerphilharmonie, Nederlands Begeleidings Orkest, Conservatory Orchestra Enschede, Neue Ruhr Kammer Philharmonie, as an assistant conductor with the Nationale Reisopera and eight years as principal guest conductor with the Nairobi Orchestra. Geluk has conducted in the Netherlands, Germany, Kenya, Czech Republic, Austria, Spain, Poland and Italy.

One particular composition of Alexander Geluk; the 'Montferland Ballade', was extremely well received both by the audience and the press, the latter one review calling it;

a 'very well composed piece of art, which appeals to the imagination' and '...Geluk is a  master of the impressionistic atmosphere...'.