In this article we present a new class of high order accurate Arbitrary-Eulerian-Lagrangian (ALE) one-step WENO ﬁnite volume schemes for solving nonlinear hyperbolic systems of conservation laws on moving two dimensional unstructured triangular meshes. A WENO reconstruction algorithm is used to achieve high order accuracy in space and a high order one-step time discretization is achieved by using the local space-time Galerkin predictor proposed in [25]. For that purpose, a new element-local weak formulation of the governing PDE is adopted on moving space-time elements. The space-time basis and test functions are obtained considering Lagrange interpolation polynomials passing through a predeﬁned set of nodes. Moreover, a polynomial mapping deﬁned by the same local space-time basis functions as the weak solution of the PDE is used to map the moving physical space-time element onto a space-time reference element. To maintain algorithmic simplicity, the ﬁnal ALE one-step ﬁnite volume scheme uses moving triangular meshes with straight edges. This is possible in the ALE framework, which allows a local mesh velocity that is different from the local ﬂuid velocity. We present numerical convergence rates for the schemes presentedinthis paperup tosixth orderof accuracyinspace andtime and show some classical numerical test problems for the two-dimensional Euler equations of compressible gas dynamics.