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We investigate the local integrability and linearizability of threedimensional Lotka-Volterra equations at the origin. Necessary and sufficientconditions for both integrability and linearizability are obtained for(1,-1,1), (2,-1,1) and (1,-2,1)-resonance. To prove sufficiency, we mainly usethe method of Darboux with extensions for inverse Jacobi multipliers, and thelinearizability of a node in two variables with power-series arguments in thethird variable.

Local Integrability and Linearizability of Three-dimensional Lotka-Volterra Systems