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We first show that every operation possesses an unique dual operation andmeasures an unique effect. If $a$ and $b$ are effects and $J$ is an operationthat measures $a$, we define the sequential product of $a$ then $b$ relative to$J$. Properties of the sequential product are derived and are illustrated interms of L\"uders and Holevo operations. We next extend this work to the theoryof instruments and observables. We also define the concept of an instrument(observable) conditioned by another instrument (observable). Identity,state-constant and repeatable instruments are considered. Sequential productsof finite observables relative to L\"uders and Holevo instruments are studied.

Dual Instruments and Sequential Products of Observables