In this paper we present an approach to analyze the direction of information flow between time series involving bidirectional relations. The intuitive idea comes from a first study dedicated to the so-called phase slope index, which is a measure originally developed to detect unidirectional relations and is based on the complex coherence function. In order to detect bidirectional flows, we propose two new causality indices supplying the previous index with two other functions, the directed coherence function and the directed transfer function. Moreover, to cope with the inability of the approaches based on coherence (ordinary or directed) or on directed transfer function to distinguish between direct and indirect relations, we propose another causality index based on the partial directed coherence to identify only direct relations. Experimental results show that some challenges have promising solutions through the use of this new indicator dealing with both linear and nonlinear multivariate models.