Abstract. This talk considers algebraic invariant curves of two-dimensional Lotka-Volterra systems. We introduce the concept of algebraic multiplicity at singular points and establish a relation between algebraic multiplicities and upper bounds of possible degrees of irreducible algebraic curves of the systems. Using the relation we explicitly give the upper bounds and derive a necessary and sufficient condition for the existence of nontrivial irreducible algebraic invariant curves of the systems whose parameters satisfy a certain generic condition.