A seismic construction system for a cavity wall is disclosed. The system is shown in three exemplary applications--a masonry backup wall with ladder- or truss-type reinforcement cooperating with a snap-in wire tie; a masonry backup wall with ladder- or truss-type reinforcement with a high-span wall anchor cooperating with a low-profile, snap-in wire tie; and a drywall backup wall with internal insulation, a sheetmetal wall anchor, and snap-in wire ties. The snap-in wire ties accommodate a continuous reinforcing wire for the outer wythe, which reinforcing wire snaps into the wire housings therefor with a predetermined force. With the interconnected wall and veneer anchors and the respective reinforcing elements a seismic construct is formed.