In many countries, stock markets are segmented to allow firms to issue shares that attract foreign funds while minimizing risk of market destabilization and loss of ownership control to foreign investors. Under these condition, two classes of shares are normally issued: restricted shares that can be traded by foreign investors, and unrestricted shares that can be traded by local investors. For example, foreign investors cannot hold voting stocks beyond 5% in Brazil and foreign investors can invested in ‘Alien Board’ and local investors can invested in ‘Main Board’ in Thailand. Local investors can hold A shares, foreign investors are allowed to invest in B shares in mainland China, and investors in Hong Kong can invest H shares. There are two equity classes of A share and B share in Norwegian market. The shares have identical cash flows, with equal claims to dividends. However, A share is fully voting, the B share has no voting rights. Although it is not a formal regulation, the Oslo Stock Exchange encouraged listed companies to simplify their share structure. Many firms have therefore merged their A and B share classes. Most of the non-voting B shares disappeared in 2001 or 2001, and only four listed firms with B shares left in 2005. Among these four companies, data up to 2012 years are available for three companies of HAFSLUND (HNA), ODFJELL (ODF), and ILHS.WILHELMSEN HDG (WWI). The price differential between A and B shares are more intense for HNA than for ODF and WWI during the sample period of January 1 of 1992 through July 31 of 2012. This paper divides the whole sample period into two sub-periods, the period of high price differential (October 1 of 1999~April 1 of 2002) and that of low price differential (July 1 of 2010~July 31 of 2012) with respect to HNA differential pattern. This paper is the first to directly examine the price information transmission effect with respect to the Oslo Stock Market (OSE) in Norway. We employ the two models of GJR-GARCH(1,1)-M model and Granger causality model. The first model allows us to examine both pricing transmission spillover effect and the volatility spillover effect between A share and B share prices. The second model allows us to investigate the causal effects between A and B share prices. The results of GJR-GARCH(1,1)-M model show that returns transmission effects are significant all the cases, and volatility transmission effects are more intense from the B share to A share than from A share to the B share. The results of the first model also report that information spillover effects are more intense in the high price differential period compared with in the low price differential period. The results of Granger causality model show that the A share cause the B share and vice versa for the whole sample period. But the second show that the B shares cause the A shares only for the sub-sample period of high price differential. The results of the two models are basically same. In sum, the price differential between A and B shares impacts the price information transmission, the information of relatively cheap non-voting B shares cause relatively expensive voting A shares. The number of sample firms of this study is inevitably small and this study uses daily data. In the future, intraday data is more desirable for this kind of study.