From a sample of about 160k Z→τ+τ− candidates collected with the ALEPH detector at LEP between 1991 and 1995, τ lepton decays involving K0S→π+π− are studied. The K0SK0L associated production in τ decays is also investigated. The branching ratios are measured for the inclusive decay B(τ−→K0SX−ντ)=(9.70\pm0.58±0.62)×10−3 , where X− can be anything, and for the exclusive decays B(τ−→K¯¯¯0π−ντ)=(8.55±1.17±0.66)×10−3, B(τ−→K¯¯¯0π−π0ντ)=(2.94±0.73±0.37)×10−3, B(τ−→K¯¯¯0K−ντ)=(1.58±0.42±0.17)×10−3, B(τ−→K¯¯¯0K−π0ντ)=(1.52\pm0.76±0.21)×10−3. The decay τ−→K0SK0Lπ−ντ is studied for the first time, giving a branching ratio B(τ−→K0SK0Lπ−ντ)=(1.01±0.23±0.13)×10−3. The channels τ−→K0SK0Sπ−ντ , τ−→K0SK0Sπ−π0ντ , τ−→K0SK0Lπ−π0ντ , τ−→K¯¯¯0π−π0π0ντ , τ−→K0K−π0π0ντ and τ−→K0h+h−h−ντ are also investigated. In addition, mass spectra in the K0Sh− and K0Sh−π0 final states are analysed to provide information on the intermediate states produced in the decays.