Mechanical systems that include reciprocating elements or modules need special attention to balance as properly as possible; they will be designated of high dynamibility when smoothly operating at high speed. Well known examples of such systems are internal combustion reciprocating-piston engines, reciprocating-piston pumps and motors, high speed punch presses and mechanical deep-drawing presses. The problem of dynamic equivalence of the engine connecting rod to two point masses to be exactly located at the piston pin and the big end centers is presented in sufficient detail, for the balancing calculations of the complete engine to be exact. Balancing short-stroke reciprocating masses, especially of high speed punch presses, is treated in its different strategies; with its different objectives. The characteristics of some categories of (low speed) intermittently reciprocating systems, in particular servo-presses for deep-drawing operations as well as sea wave energy harvesting systems are presented.