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Where can you find dividends for Australian Stock Market Shares (ASX) for more than 2 years of data? 
You can register with an online broker. You can usually join most online brokers for free and only have to fund your account if you decide to place a trade. You may also check out the website of the actual companies you are interested in. They will provide current and historic data of the company's financials. For BHP you can click on the link at the bottom of this webpage to get a PDF file of past dividends from 1984.