Abstract <p>Tricomi–Gaussian beams (TGBs) belong to the class of non-diffracting Tricomi light beams with finite cross-section and finite energy. So, in this work, a theoretical investigation of propagation characteristics of TGB in a strongly nonlocal nonlinear medium (SNNM) has been conducted. SNNM is well-known for its nonlinear optical response at a specific location, and it can be affected by an electromagnetic field that extends across a large spatial region. The propagation problem is addressed by expressing the TGB fields in SNNM with the help of the extended Huygens–Fresnel diffraction integral formula and the optical ABCD matrix system. To analyze its propagation dynamics, the effects of different configuration parameters of TGB, such as topological charge, waist radius, and propagation distance, are meticulously examined. The diverse cases like as on-axis, off-axis, and asymmetrical Bessel Gaussian beams can be achieved as special cases by appropriately selecting the complex beam parameters of TGB. This work will be helpful to study and analyze the electromagnetic radiation force, scattering and propagation, optical manipulation, computer-generated holography, light–matter interaction, and optical tweezers and sensors.</p>