We propose a global network model to investigate the interdependence among the oil-equity nexuses from different countries in various time horizons based on wavelet coherence and gray correlation. The stock indexes from 28 countries and crude oil prices of WTI (West Texas Intermediate price) and Brent are the sample. We obtain the following primary results: Oil-equity nexuses throughout the world are well-integrated across time scales; Ireland, the Netherlands, Norway, Singapore, Demark, Germany and the Czech Republic for Brent-stock nexuses and Ireland, the Netherlands, Netherlands, Singapore, Japan, Germany and Malaysia for WTI-stock nexuses, successively corresponding to the frequency bands of 4 days-256 days, can be treated as a benchmark and can spread their fluctuations to other nexuses easily and rapidly. By contrast, China is more isolated in most time horizons and could be the ideal risk-hedging choice. Next, the global interdependence among oil-stock nexuses is characterized by the clustering effect, by which geographical factors and the oil production-consumption profile can exert their influence in most time horizons. In contrast, the speculation deals as well as energy policy and stagey are primarily influential in certain frequency bands. Thus, the decision-making for different time horizons could consider corresponding references. (C) 2016 Elsevier Ltd. All rights reserved.