00-08E

We study the scaling properties of self-avoiding walks (SAWs) on a $d$-dimensional disordered lattice with quenched defects obeying a power law correlation $\sim r^{-a}$ for large distances $r$. Such type of disorder is known to be relevant for magnetic phase transitions. We apply the field-theoretical renormalization group approach and perform calculations in a double expansion in $\varepsilon =4-d$, $\delta =4-a$. The asymptotic behaviour of SAWs on a lattice with long-range-correlated disorder is found to be governed by a new exponent $\nu ^{long} =1/2+\delta /8,\mskip \thickmuskip (\varepsilon /2<\delta <\varepsilon )$. This is to be compared with a first order result for SAWs on a "pure" lattice: $\nu ^{pure}=1/2+\varepsilon /16,\mskip \thickmuskip (\varepsilon >0)$.