CFTP now has 14 permanent members, plus 12 postdoctoral fellows with PhD. About two-thirds of the permanent members have tenure positions at Instituto Superior Técnico, while three of the permanent members belong to other universities. The postdoctoral fellows are mostly nationals from other countries. CFTP also has several PhD students working under the supervision of permanent members of the Centre.

All important decisions of the Centre are made by the Scientific Committee. This committee includes all permanent members.

The Executive Committee (EC) takes care of all daily business:

Present members of the EC:
Gustavo Castelo-Branco (chairman)
Luis Lavoura
Teresa Peña
M.N. Rebelo
Jorge Romão
Joaquim Silva-Marcos