In this letter we extend previously established results for nested carbon nanocones to both nested boron nitride and carbon-boron nitride nanocones. Based purely on mechanical principles and classical mathematical modelling techniques, we determine the energetically favourable structures for nested boron nitride and carbon-boron nitride nanocones. While only three apex angles for boron nitride tend to occur, we also consider the other two angles corresponding to the equivalent carbon nanocones. Two nanocones are assumed to be located co-axially in a vacuum environment. The Lennard-Jones parameters for boron nitride and carbon-boron nitride systems are calculated using the standard mixing rule. For the boron nitride cones, numerical results indicate that the interspacing between two cones is approximately 3.4 A ° which is comparable with the experimental results. For the hybrid carbon-boron nitride cones, the numerical results essentially depend on the outer cone angle, and the interspacing distance is also obtained to be approximately 3.4 A ° . Moreover, the equilibrium position is such that one cone is always inside the other, and therefore nested double-cones are possible in practice.