Summary: The paper deals with the following question: Which semialgebraic subsets of \(\mathbb{R}^n\) can be realized as tangent cones to real algebraic subsets of \(\mathbb{R}^n\)? At first we prove that the answer is positive for every closed semialgebraic cone in \(\mathbb{R}^n\) of dimension \(\leq 2\). Then, for closed semialgebraic cones \(A\) in \(\mathbb{R}^n\) admitting a sufficiently nice algebraic presentation, we explicitly give equations of an algebraic subset \(Y \subseteq \mathbb{R}^n\) having \(A\) as its tangent cone.