A set of p-valued logic gates (primitives) is called universal if an arbitrary p-valued logic function can be realized by a logic circuit built up from a finite number of gates belonging to this set. In the paper, we consider the problem of determining the number of universal single-gate libraries of p-valued reversible logic gates with two inputs and two outputs under the assumption that constant signals can be applied to arbitrary number of inputs. We have proved some properties of such gates and established that over 97% of ternary gates are universal.