In the paper I discuss theoretical differences between left and rightlibertarianism. (I will skip the specific and practical issues which differ left and rightlibertarians, including among others the minorities and immigration policies or affirmative action. I assume that practical solutions suggested by the followers of both positions stem from their theoretical assumptions.) I will focus on two issues which determine the fundamental difference between left and rightlibertarianism. These are property and equality. I compare standpoints of some leftlibertarians with the positions of rightlibertarians represented by Murray Rothbard, concerning property and equality. I conclude that the main and fundamental difference between leftand rightlibertarians concerns equality. Leftlibertarians are egalitarians whereas rightlibertarians are antiegalitarians. I also argue that egalitarian position is not compatible with the notion of full selfownership, which leftlibertarians advocate for.