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The stability problem of stochastic networks with proportional delays and unsupervised Hebbian-type learning algorithms is studied. Applying the Lyapunov functional method, a stochastic analysis technique and the It<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover accent="true"><mi>o</mi><mo stretchy="false">^</mo></mover></semantics></math></inline-formula> formula, we obtain some sufficient conditions for global asymptotic stability. We also discuss the estimation of the second moment. The correctness of the main results is verified by two numerical examples.