The quark model does not exclude states composed of more than three quarks, like pentaquark systems. Controversial evidence for such states has been published in the last years, in particular: for a strange pentaquark Θ(1540)+; for a double-strange state, the Ξ(1862)−−, subsequently called Φ(1860)−−; and for a charmed state, the Θc(3100)0. If confirmed, a full pentaquark family might exist; such pentaquark states could be produced in e+e− annihilations near the Z energy. In this Letter a search for pentaquarks is described using the DELPHI detector at LEP, characterized by powerful particle identification sub-systems crucial in the separation of the signal from the background for these states. At 95% CL, upper limits are set on the production rates N of such particles and their charge-conjugate state per Z decay: , NΘ++<1.6×10−3, NΦ(1860)−−×Br(Φ(1860)−−→Ξ−π−)<2.9×10−4, .