Good question, but before I take a stab at answering it, take a look at your question and replace "Native Americans" with "people," and you'll start to see how incredibly broad and impossible to answer this is without years of research and a book-length dissertation.

That doesn't mean it's not a good question -- it's just too broad for me to cover all Native Americans. So let me narrow things down to the Alutiiq/Sugpiaq of the Kodiak archipelago in southwestern Alaska.

I'm going to rely on two principal sources: Kodiak Kreol: Communities of Empire in Early Russian America by Gwenn Miller, and Looking Both Ways: Heritage and Identity of the Alutiiq People (several authors). These are good secondary sources that will give you plenty of links to primary sources and additional reading if you want to dig further.

OK. With the preliminaries out of the way, let me say that before contact with the Russians in the 18th century, the Alutiiq did not break things down into discrete months/weeks/days/hours/minutes/seconds. That's a modern innovation, borne of the need for accurate navigation and industrialization. In Nanwalek, there are traditional words for summer (kiak), fall (uksuaq), winter (Uksuq) and spring (iciwaq), but the modern Alutiiq dictionary also includes words for the months and so forth. For example, February is Nanic'aaq Iraluq, literally "shortest moon." It's important to make this distinction: Alutiiq culture is just as alive as Irish, German or American culture. Adaptation takes different forms in different places.

For the prehistoric Alutiiq, time was cyclical, possibly because life revolved around the return of the salmon each summer to Alaska's rivers. Salmon were (and still are) life: They provide food and a means of trade, even today. Before the Russians arrived, Miller writes, "Alutiiq men spent most of their time during summer and autumn hunting whales and fur-bearing animals, primarily sea otters and the great Kodiak bears (for few other land animals roamed the island)."

Salmon returned to the rivers each summer, which required preparing fish traps. Offshore, halibut and cod could be caught. Before the whalers went offshore (imagine hunting a whale in a one-man kayak!) in June and July, there were hunting festivals to celebrate the return of the fish and the end of spring, usually the hungriest season of the year. Women and children helped prepare and preserve food for winter, as well as gather berries and prepare tools.

During the winter, men hunted bears in their dens and fished with their children. Women wove and sewed, and the cycle repeated in the following year.

What about time?

"Every society has a concept of time, a way of thinking about the past that orders the universe and ties people together. Westerners tend to think of time as linear -- tracking the evolution of species, charting the progress of industry, and following family histories from one generation to the next. Gordon Pullar suggests that time is circular and more fluid for the Aluttit. From this perspective, the past is part of the present, and events from distant times continue to inform daily life and shape the future."

Time is closely linked to spirituality and myth (unigkuat) that explain how the universe began. Alutiiq stories, collected by the Russians in the 18th and 19th centuries, suggest the people who lived in Kodiak and the rest of Alaska -- though they lived a cyclical life -- had a firm notion of where they came from. In Kodiak, the stories tell of a migration from the north. In 1873, Alphonse Pinart wrote of a "Koniagmiut" (Kodiak Alutiit) story that explains that when they arrived in Kodiak, the archipelago's inhabitants crossed the Shelikof Strait at a time when it was barely wider than a stream. That's something that could have happened during the last ice age, when sea levels were much lower.

Thus, even though they may not have had a modern time sense, the Alutiiq had a sense of time. The seasons may have been cyclical, the salmon may have returned each summer without end, but they had a strong sense that things were spiraling forward, that there was an origin at some point.