The need for low-power alternatives to digital electronic circuits has led to increasing interest in logic devices where information is stored in nanomagnets. This includes both nanomagnetic logic, where information is communicated through magnetic fields of nanomagnets, and all-spin logic (ASL), where information is communicated through spin currents. A key feature needed for logic implementation is nonreciprocity, whereby the output is switched according to the input but not the other way around, thus providing directed information transfer. The objective of this paper is to draw attention to possible ASL-based schemes that utilize the physics of spin-torque to build in nonreciprocity, as in transistors, that could allow logic implementation without the need for special clocking schemes. We use an experimentally benchmarked coupled spin-transport/magnetization-dynamics model to show that a suitably engineered single ASL unit indeed switches in a nonreciprocal manner. We then present heuristic arguments explaining the origin of this directed information transfer. Finally, we present simulations showing that individual ASL devices can be cascaded to construct a ring oscillator circuit, which provides a clear signature of inbuilt directionality.