Distance scale and variable stars in Local Group Galaxies: LMC and Fornax

We briefly review our photometric and spectroscopic study of RR Lyrae variablestars in the bar of the Large Magellanic Cloud(LMC), that allowed us to reconcile the so-called "short" and "long" distance moduli of the LMC on the value mod_LMC=18.51 +/- 0.085 mag. Then we present preliminary results from the photometric study of a 33' x 34' area in the Fornax dwarf spheroidal galaxycontaining the stellar clusters Fornax 3 (NGC 1049) and 6. We identified about 1000 candidate variables in this field of Fornax, and report the first detection and measure of about 60 RR Lyrae variablestars in the globular clusterFornax 3.