Aristar Inc., a Miami-based consumer finance and furniture company, yesterday announced its intention to acquire American Finance System Inc., a consumer finance corporation with headquarters in Silver Spring. Aristar offered $9.50 cash for each AFS share. When trading was halted last Friday, AFS closed at $7.625.

This is the second time around for Aristar and American Finance. Back in 1975, they announced a merger but it fell through because financing could not be obtained for combined operations in which AFS would have been the surviving entity. Both companies then were in serious financial difficulty as the result of high interest rates.

Then Gamble-Skogmo Inc., a mass merchandiser, bought a half interest in Aristar. Following a $7.8 million loss in fiscal 1976, Aristar had a $1.9 million profit for the year ending June 30. In the next six months, earnings soared to $3.3 million. Then Aristar decided to renew its interest in America Finance, this time seeking control. This year it has bought 4.8 percent of AFS' outstanding common stock.

But Aristar may have to contend with Security Pacific Corp., a giant Los Angeles bank holding corporation. Last month, it signified its desire to take over all AFS stock through a transfer of 0.2617 share of Security Pacific for each share of AFS. The offer amounted to about $7.85 a share of AFS common stock, tax free.

Security Pacific also offered $25.25 cash plus accumulated dividends amounting to $3.75 for each share of AFS preferred stock.

American Finance's board of directors approved the Security Pacific offer last month and will meet tomorrow to consider the Aristar bid. A spokeswoman for Security Pacific said yesterday the company is "continuing actively to pursue our negotiations and discussions."

AFS has been the object of several takeovers in recent years. In 1973, First Chicago Corp. tried but withdrew when the Federal Reserve objected to a bank holding company expanding into the consumer finance field. (Since then it has yield, and Security Pacific bought a consumer firm in 1976.) In 1976, Beneficial Corp., another consumer finance firm, was deterred from taking over AFS when the Justice Department indicated objections on antitrust grounds.

Since the first Aristar proposal, American Finance has slimmed down from about 750 branch offices to 370. It reported steep net losses of $14.8 million in 1975 but once again is in the black. For the nine months ending Sept. 30, AFS earned $5.4 million (1.07 a share , an extraordianry item) compared with $1.8 million (29 cents) the year before.