Infinite Sequential Truels are studied in the case when the players' duel values are preassigned parameters, rather than functions of the marksmanships. Such truels divide naturally into two classes, one of which includes all Infinite Sequential Truels investigated previously. All equilibrium points of all truels are determined. It is discovered that some truels possess one or several of four equilibrium points never before observed, and that others may possess no equilibrium points at all (in stationary strategies).