The two-part curable composition has excellent curability, and exhibits flexibility and adhesion durability. The two-part curable composition includes a first reagent containing at least a 2-cyanoacrylic acid ester and a second reagent containing at least a polymer having a hydrolyzable silyl group, in which an elastomer and a curing catalyst for the above polymer are each contained in at least one of the first and second reagents in predetermined amounts. A preferable curing catalyst is a compound having a metal element and an organic group bonded to the metal element via oxygen, or an acid having a pKa of 4 or lower at 25° C. Preferably, a curing accelerator for 2-cyanoacrylic acid ester is contained in at least one of the first and second reagents.