The effects of transition-metal (TM) impurities on the transition temperature of an anisotropic superconductor when the TM impurities give rise to local spin fluctuations (LSF's) are studied. The effective electron-electron interaction between the Cooper-pair electrons is taken to be the sum of a separable anisotropic electron-phonon potential and the repulsive Coulomb potential existing between the electrons. The multiplicative renormalization technique is used to treat the Coulomb repulsion between the d electrons of opposite spins which localize about an impurity site. It is found that the LSF's infiuence the anisotropic superconductors in two ways. They cause a decrease in the anisotropy and an increase in the Coulomb pseudopotential, Numerical calculations of the decrease in T, are carried out using parameters appropriate to the dilute AlMn superconductors.