  We consider a nonlinear Dirichlet problem driven by the $(p,q)$-Laplacian and
with a reaction having the combined effects of a singular term and of a
parametric $(p-1)$-superlinear perturbation. We prove a bifurcation-type result
describing the changes in the set of positive solutions as the parameter
$\lambda>0$ varies. Moreover, we prove the existence of a minimal positive
solution $u^*_\lambda$ and study the monotonicity and continuity properties of
the map $\lambda \to u^*_\lambda$.
