In 1992, Veldman started her own dance company called Alias with Guilherme Botelho. The first work En Manque was performed to great acclaim in London, Glasgow, Zurich and Lausanne. The production also won two major choreographic awards: the Dance Exchange International 1993 and the Prix romand des spectacles indépendants 1994. Veldman left Alias after an invitation by Christopher Bruce to join Rambert Dance Company in 1994.
Whilst being a dancer with Rambert Dance Company, Veldman created three works for the repertory. She received a grant from the Choo-San Goh & H. Robert Magee Foundation for her third production with Rambert. This production also won the Lindbury Prize for Stage Design created by Miriam Buether.
Veldman left Rambert in 2000 to concentrate on her choreographic career. She has created a big variety of works, full evening story telling works with symphony orchestra and smaller creations as part of a triple bill. She has worked for companies all over the world like; Les Grands Ballets Canadiens de Montréal, Portugal's Ballet Gulbenkian, Cedar Lake Contemporary Ballet of New York, United Kingdom's Rambert Dance Company, Sweden's Cullberg Ballet, Royal New Zealand Ballet, Ballet Bern, Komische Oper Berlin, Netherlands' Introdans and Iceland Dance Company amongst others.
Since 2000 she has built up a relationship with Les Grands Ballets Canadiens, which she is immensely grateful for. This has allowed her to deepen her choreographic work together with their wonderful dancers. She has worked with the company on 8 separate occasions.