GaN epilayers have been grown by plasma-assisted molecular-beam epitaxy on ZrB2 substrates with close in-plane lattice match. Growth processes utilizing both low-temperature GaN (LT-GaN) and AlN nucleation layers were investigated. The x-ray ω-scan widths for the optimized LT-GaN nucleation process were 400 and 750 arcsec for symmetric and asymmetric reflections, respectively. When using LT-GaN nucleation layers, the chemical incompatibility of ZrB2 results in a high dislocation density despite the in-plane lattice match. The epilayer polarity was N-polar for LT-GaN nucleation layers under all conditions investigated. For AlN nucleation layers, Ga-polar epilayers were obtained under suitable conditions (Al-rich, lower nucleation temperatures) for nominal AlN thickness as low as 1 nm. From RHEED analysis it appears that a psuedomorphic Al wetting layer forms on the ZrB2 surface, and that using AlN as the nucleation layer may offer promise for reducing the epilayer defect density.