The Amyraldian, or Amyraldism, follows the teachings of Moyse Amyraut, who, according to Curt Daniel, “posited that Christ died for all men because of universal grace. Christ died equally for all in order to provide a basis for the universal part of the Covenant of Grace. This provision was universal, but the application was particular and limited to the elect. Amyraut felt that this was the view of Calvin and the early Reformers.” This is also called Hypothetical Universalism (but the general atonement version of Hypothetical Universalism appears to be different from Amyraut’s Hypothetical Universalism, in my opinion). “The theory basically is…two kinds of grace: universal grace for all men and special grace only for the elect. Because of universal grace and the universal aspect of the Covenant of Grace, it is hypothetically possible for the heathen to be saved without hearing the Gospel…in fact none of these have ever been saved because it is only through the Gospel that saving faith is given. Further, God is said to have two wills: a universal conditional will and a particular unconditional will.”
The view of Andrew Fuller (Fullerism) seems to accord well with Amyraldism (or Amyraldianism) and is often so called. Fuller reasoned that on the one hand, Christ died to atone for all men; and on the other hand, as the Father saw in advance that no one would wish to accept Christ of their own free will, He only guaranteed that certain sinners would follow their inner sense of duty and repent and believe. Christ still died for all men, though His Father restricted salvation to the elect. The thought that “Christ’s death is sufficient for all, but efficient for only the elect” is part of this system.