Purpose: Distinguishing persistent from permanent atrial fibrillation (AF) in a reliable way would improve AF patient management, as cardioversion options could be considered appropriately. In this study, complexity measures based on the combined analysis of multiple surface ECG leads were tested to classify persistent or permanent AF. Methods: 53 patients diagnosed with persistent (N=20) or permanent (N=33) AF were studied. Multidimensional spectral analysis was performed on each possible combination of precordial ECG leads (V1 to V6) using the so-called spectral envelope. This method detects and emphasizes any oscillatory component common to several ECG leads. On resulting spectra, multivariate organization index (MOI) and multivariate spectral entropy (MSE) were computed to assess AF organization. These measures were used to classify persistent and permanent AF via quadratic discriminant analysis. Multivariate methods were compared to their univariate counterparts, i.e. organization index (OI) and spectral entropy (SE) computed on a single ECG lead. Results: Multivariate complexity measures were able to accurately distinguish persistent and permanent AF with correct rates up to 88.7%. The predictive value for permanent AF was 96.6%. MOI was significantly lower in patients with permanent AF compared to patients with persistent AF (p<0.01), indicating that global atrial organization was lower during permanent AF compared to persistent AF. In comparison, univariate OI and SE could not demonstrate a change in organization between persistent and permanent AF, and the best correct rate was 67.9%. Conclusions: Non-invasive multivariate complexity measures identify the global organization of atrial activity more accurately than univariate ones. The proposed analysis framework could potentially provide automatic methods to distinguish persistent from permanent AF through surface ECG analysis. Such information could be of valuable importance in clinical settings, patient management and therapeutic decisions.