Discrete event systems (DESs) are considered for which faulty behaviour occurs ``intermittently'', with fault events \(f_i\), \(i=1,\dots,m\), followed by reset events \(r_i\), \(i=1,\dots,m\), followed by new occurrences of fault events, and so forth. Since these events are usually unobservable a diagnostic methodology for intermittent faults is developed. The methodology uses the notions of \(\Sigma_f\)-recurrent and \(\Sigma_r\)-recurrent languages which imply that fault and reset events occur with some regularity along any possible path of the DES's evolution. It is also assumed that there are observable events between some pairs \((f_i,r_i)\) and \((r_i,f_i)\) for any cycle in the system. In the article some new notions of diagnosability are introduced. These notions imply that the knowledge of observable events allows us to identify the instances where we are certain that faults are present or absent in the system. The associated necessary and sufficient conditions are based upon a technique of ``diagnosers''. The diagnosability conditions are verified in polynomial time in the number of states of diagnosers. Results are illustrated by an example.