If your country of origin allows dual citizenship you should be allowed to keep both. Citizenship is simple at this point, but is subject to change, so you may wish for an agent/lawyer to monitor your eligibility as time goes on. Simply, rules of citizenship eligibility are: three years out of four years of stay in Australia and the last nine out of 12 months of stay must be as an Australian PR. Exemptions may apply.
What standards are applied to maintain permanent resident status and eventually receive Australian citizenship?
I am working on an investor stream application and wish to relocate my family to Australia. However, I don’t want to completely abandon my country of origin, as I still have family and business ties there. Can I live in both? What residency requirements are there for maintaining my presence in Australia so I can become a permanent resident and then a citizen?
In order to secure your PR for investor stream, you will need to hold your subclass 188 investor stream for at least four years and maintained the complying investment of 1.5 million with state bonds during your visa duration and have lived in Australia for at least two years during your 188 visa period. Upon grant, the investor stream PR visas, like any other PR visas, would require you live in Australia for a minimum of two out of five years in order to qualify for a repeat five-year resident return visa (which is your travel facility). Yes, you can still continue living in both countries as long as you fulfill your minimum residential requirements to ensure your RRV grant every five years. To be eligible for citizenship, you need to: have lived in Australia on a valid Australian visa for four years immediately before applying; must hold your PR for the 12 months immediately before making an application and not have been absent from Australia for more than one year in total, during the four year period, including no more than 90 days in the 12 months before applying.
These visas are quite complicated, but to answer your question, yes, you can live in two countries.
If you are applying in the 188B investor stream you will need to reside in Australia for at least two of the four years before applying for permanent residency under the 888 visa category. The residency requirements to be eligible to apply for citizenship are four years of residency in Australia and at least 12 months as a permanent resident.