02-07E

In agreement with the Harris criterion, {\em asymptotic} critical exponents of three-dimensional (3d) Heisenberg-like magnets are not influenced by weak quenched dilution of non-magnetic component. However, often in the experimental studies of corresponding systems concentration- and temperature-dependent exponents are found with values differing from those of the 3d Heisenberg model. In our study, we use the field--theoretical renormalization group approach to explain this observation and to calculate the {\em effective} critical exponents of weakly diluted quenched Heisenberg-like magnet. Being non-universal, these exponents change with distance to the critical point ${\rm T_c}$ as observed experimentally. In the asymptotic limit (at ${\rm T_c}$) they equal to the critical exponents of the pure 3d Heisenberg magnet as predicted by the Harris criterion.