An offset matrix adapter for integrating existing components of K'nex construction toys with existing components of Lego-style brick systems, notwithstanding that the spacing matrices of the systems are incompatible. Adapter bricks or bases are provided, having adapter sockets with the same spacing matrix as the studs of the Lego-style bricks. Special K'nex offset matrix adapters are provided, consisting of a pair of spaced-apart mounting stems for reception in a pair of spaced-apart adapter sockets. An offset rod is rigidly supported at the tops of the mounting stems but is offset laterally from the axes of the mounting stems by a distance which is preferably about one-third of the spacing between adapter sockets. By orienting a pair of matrix adapters with the rods offset alternatively inward or outward, the spacing differences between K'nex and Lego-style systems can be reduced to insignificance, allowing the two systems to be easily integrated.