This paper presents a strategy for deadlock avoidance of mobile robots in narrow passages of environments populated with other moving objects. The proposed strategy detects deadlocks in narrow passages only by robot's perceptive sensors, i.e., no other communication means with moving objects is assumed. The strategy is based on the random multi-access algorithm for the network congestion avoidance. The strategy is implemented within our existing motion planning and control system for mobile robots and thoroughly tested by simulation and experimentally on the Pioneer 3DX mobile robot equipped with SICK LMS-200 laser range finder. The test results illustrate the appropriateness of the proposed strategy for resolving deadlocks in narrow passages.