The only case where you can claim a win is a checkmate, but you don't have to: the system grants you the win without any interaction.
On OTB situations, there is an arbiter who is involved, and he could/should tell whether a player makes illegal moves on purpose, or not.
According to the rules, an illegal move involves time punishment.
I was playing an over the board chess match yesterday, blitz competetion, 10 minute on each clock. Anyway the problem i am having is that i feel like i was cheated... Now on the last game i was down on time, but in an entirely winning position, anyway i was close to checkmate, opponents position hopeless, only a few pieces left on the board. Anyway the problem i having,ok, imagine this, me with 10 seconds left on chess clock, only a few moves of checkmate, then oppenent plays illegal move, presses his clock and as i correct him, i loose valuable few seconds off my clock, and eventually with like i move of checkmate loose the game on time, could i have claimed a win at the moment my oppenent played illegal move wasting my time, if so do i stop the clocks or just leave my clock running. please help!