We present the results of a systematic search for old isolated neutron stars (ONS) in the direction of two giant molecular clouds in Cygnus (Rift and OB7). By analyzing ROSAT PSPC pointings, we find four sources with no measurable optical counterpart within their error circle in the digitized red plates of the Palomar All Sky Survey. Their count rates ((similar to 10(-3) c s(-1)) and spectral properties are also consistent with the hypothesis that the X-ray emission is produced by ONSs. Comparison with the number of sources expected on the basis of theoretical calculations indicates that the assumptions and/or the range of parameters of theoretical models need to be revised.