The first, to introduce a complete ban on the practice, looks set to be defeated.
But the second, which proposes limiting assisted suicide to Zurich residents only, could get more support.
The Swiss are uneasy that so many foreign citizens are coming to Switzerland because assisted suicide remains illegal in their own countries.
In Switzerland the individual right to decide is hugely important, says the BBC’s Imogen Foulkes in Geneva.
The system of direct democracy, in which the people vote on all major political decisions, is a sign of that, she says.
So too is the fact that assisted suicide – or as the Swiss see it, the right to choose when and how to die – has been legal for decades, our correspondent adds.
While opinion polls indicate a majority of Swiss remain in favour of assisted suicide, they also suggest that 66% are against what has become known as suicide tourism.
Bernhard Sutter, of Switzerland’s biggest assisted suicide organisation Exit, says Europe is simply exporting its moral dilemmas.
“We cannot solve the dying problems of the rest of Europe,” he said. “And we think it is very sad that very ill people have to travel thousands of kilometres to go to a liberal country to die there.
“These other countries should solve their own problems with dying people, so we would be happy if Germany, or Great Britain, would change their laws.”
Already Exit will only assist those who are permanently resident in Switzerland – saying the process takes time, and much counselling for both patients and relatives.
Zurich’s vote on the issue will be watched very closely by the Swiss government, which is currently revising Switzerland’s federal laws on assisted suicide.