Fault-tolerant systems have found wide applications in military, industrial andcommercial areas. Most of these systems are constructed by multiple-modular redundancy or er-ror control coding techniques. They need some fault-tolerant specific components (such as voter,switcher, encoder, or decoder) to implement error-detecting or error-correcting functions. However,the problem of error detection, location or correction for fault-tolerance specific components them-selves has not been solved properly so far. Thus, the dependability of a whole fault-tolerant systemwill be greatly affected. This paper presents a theory of robust fault-masking digital circuits forcharacterizing fault-tolerant systems with the ability of concurrent error location and a new schemeof dual-modular redundant systems with partially robust fault-masking property. A basic robustfault-masking circuit is composed of a basic functional circuit and an error-locating corrector. Sucha circuit not only has the ability of concurrent error correction, but also has the ability of concurrenterror location. According to this circuit model, for a partially robust fault-masking dual-modularredundant system, two redundant modules based on alternating-complementary logic consist of thebasic functional circuit. An error-correction specific circuit named as alternating-complementarycorrector is used as the error-locating corrector. The performance (such as hardware complexity,time delay) of the scheme is analyzed.