"We study quasiminimizers of the following anisotropic energy (p, q) - Dirichlet integral \int_\Omega ag_u^p dmu + \int_\omega bg_u^q dmu in metric measure spaces, with g_u the minimal q-weak upper gradient of u. Here, \Omega\in X is an open bounded set, where (X, d, µ) is a complete metric measure space with metric d and a doubling Borel regular measure µ, supporting a weak (1, p)-Poincar´e inequality for 1 < p < q. We consider some coefficient functions a and b to be measurable and satisfying 0<\alpha\leq a, b \leq \beta, for some positive constants \alpha,\beta. Using a variational approach we study interior regularity for quasiminimizers of a (p, q)-Dirichlet integral, as well as regularity results up to the boundary. We extend local properties of quasiminimizers of the p-energy integral on metric spaces studied by Kinnunen and Shanmugalingam [3] to an anisotropic case. For the interior regularity, we use De Giorgi type conditions to show that quasiminimizers are locally H¨older continuous and they satisfy Harnack inequality, the strong maximum principle and Liouville’s Theorem. Furthermore, we give a pointwise estimate near a boundary point, as well as a sufficient condition for H¨older continuity and a Wiener type regularity condition for continuity up to the boundary. Finally, we consider (p, q)-minimizers and we give an estimate for their oscillation at boundary points. This is a joint work [5] with Cintia Pacchiano Camacho (Aalto University)."