The results of highly accurate calculations are presented for all nine
of the known bound P states (L = 1) and D states (L =2) of the six th
ree-body muonic molecular ions (mesomolecules): ppmu, pdmu, ptmu, ddmu
, dtmu, and ttmu. The mass shift (mass gradient) was determined for ea
ch ion for the lowest P and D states and for the first ''vibrationally
'' excited P states. The threshold mass ratios lambda(t) = m(Y)/m(X) f
or the lowest bound P and D states in symmetric systems such as X+X+Y-
were determined, with improved accuracy, to be lambda(t)(P) = 0.237 3
4 and lambda(t)(D) = 0.0891.