Let L be a finite dimensional real Lie algebra. A wedge is a topologically closed set closed under addition and nonnegative scalar multiplication. A wedge W is called a semialgebra, if there is a Campbell-Hausdorff neighborhood B such that (W\(\cap B)*(W\cap B)\subseteq W\), where * denotes the Campbell-Hausdorff multiplication \(x*y=x+y+[x,y]+....\) ``This paper gives some basic facts on (Lie)semialgebras and shows the crucial steps that lead to a classification of semialgebras in a class of Lie algebras that contains the reductive ones. The classification of invariant wedges by Hilgert and Hofmann is a prerequisite.'' The paper contains a number of useful examples, too.