Epitaxial integration of superconductors with semiconductors is expected to enable new device architectures and to increase electronic circuit and system functionality and performance in diverse fields, including sensing and quantum computing. Herein, radiofrequency plasma molecular-beam epitaxy is used to epitaxially grow 3-200 nm-thick metallic NbN x and TaN x thin films on hexagonal SiC substrates. Single-phase cubic δ-NbN and hexagonal TaN x films are obtained when the starting substrate temperature is %800 and %900 C, respectively, and the active N to Nb or Ta ratio is %2.5-3. The films are characterized using in-situ reflection high-energy electron diffraction and ex-situ atomic force microscopy, contactless sheet resistance, X-ray diffraction, X-ray photoelectron spectroscopy, secondary ion-mass spectrometry, Rutherford backscattering spectrometry, cross-sectional transmission electron microscopy, and low-temperature electrical measurements. Smooth, epitaxial, low-resistivity films of cubic δ-NbN and hexagonal TaN x on SiC are demonstrated for films at least %50 nm-thick, and their superconducting properties are reported. Epitaxy of AlN and GaN on δ-NbN is also demonstrated, as well as integration of an epitaxial NbN x superconducting electrode layer under GaN high-electron mobility transistors. These early demonstrations show the promise of direct epitaxial integration of superconducting transition metal nitrides with group III-N semiconductors.