Pion-induced pion production on the deuteron was studied via the reactions d pp and d nn. The doubly differential cross sections for these reactions were measured, covering the center-of-mass phase space at incident pion energies of 256, 331, and 450 MeV. Calculations of the quasifree production process on one nucleon were performed in a plane-wave approximation using a phenomenological, on-shell p n amplitude. Comparison of the data with the calculations indicates that the quasifree mechanism dominates these production reactions on the deuteron. Upper limits for bound nn and pp systems with small binding energies were also measured. The possible existence of a resonance in these systems near the production threshold was investigated.