The threshold characteristics of mutually coupled SQUIDs (Superconducting Quantum Interference Devices) have been analytically and numerically investigated. The mutually coupled SQUIDs investigated is composed of an rf-SQUID and a dc-SQUID. Here, the rf-SQUID is a flux quantum generator and the dc-SQUID is a flux detector. The linearization method substituting sin-1x by (π/2)x (1x1) is found valid when it is applied to the mutually coupled SQUIDs, because it is possible to obtain the superconducting regions analytically. By computer implementation of linearization method, we found this method is very effective and very quick compared to the ordinary methods. We report the internal flux on an rf-SQUID, the threshold of a dc-SQUID, and that of mutually coupled SQUIDs obtained by Lagrange multiplier formulation and linearization. The features of the threshold characteristics of the mutually coupled SQUIDs with various parameters are also reported. The discontinuous behavior of threshold of the mutually coupled SQUIDs are attractive for digital applications. We suggest three applications of the mutually coupled SQUIDs, that is, a logic gate for high-Tc superconductors (HTSs), a neuron device, and an A/D converter.