No one should be too terribly surprised to see major market indexes moving in different directions on Monday -- especially since it's the Nasdaq Composite (NASDAQINDEX:^IXIC) that's on the rise even as the rest of the stock market pulls back from record levels. As of 3 p.m. EST, the Nasdaq was up by a third of a percent, putting it on pace to close at yet another all-time high.

Many investors are focusing their attention on the smaller, faster-growing companies that have come into the spotlight this year. Yet for the Nasdaq to deliver as good a performance in 2021 as it has in 2020, it will need additional contributions from its leaders. In particular, Apple (NASDAQ:AAPL) and Facebook (NASDAQ:FB) are working to get back their shares back to the levels they reached during the summer. If they can, it could help establish the current bull market as more than just a bounce back from the coronavirus bear market.

Metallic bull and bear figurines on top of a newspaper's stock page.

Image source: Getty Images.

Apple is trying to get back on top again

Shares of Apple were on the rise Monday, climbing more than 1%. The launch of the iPhone 12 series has been a big success, but the stock still hasn't regained the levels it reached this summer immediately following its decision to do a stock split.

The iPhone 12 is a big deal because it's the first smartphone from the tech giant that can utilize the world's rapidly expanding 5G wireless networks. But it's only the tip of the iceberg for Apple. In the third quarter, demand for wearable devices like the Apple Watch surged back upward. The launch of the Apple Watch Series 6 and SE products helped stoke greater consumer excitement about the line, and as many countries started to relax their COVID-19 restrictions, more people ramped up their outdoor activities. The fact that Apple Watches were available at a range of prices was also a plus.

Then there's the company's growing ecosystem of services. One that's getting a lot of attention lately is the Apple TV+ video-streaming platform, which is now more than a year old and starting to gain traction both creatively and among consumers. Add that to older favorites like the App Store and new initiatives like Fitness+ and the Apple One subscription plan, and you can see why investors like what they're seeing on the services side.

Apple soared during the past couple of years, and few would describe the stock as value-priced right now. But it's below where it traded in early September, and that leaves it with some room to move higher even without the stock reaching new record levels.

More than a pretty face

Facebook was up more than 2% Monday afternoon. The social media powerhouse also hit record highs during the summer, but it has spent the last few months treading water.

Much of the challenge for Facebook has come on the regulatory side. Lawmakers haven't liked what they've seen from the company, and there are growing concerns that it hasn't done enough to monitor the content on its platform. Related to that, some advertisers are boycotting Facebook, which could curtail its revenue growth. A recent anti-discrimination lawsuit filed by the Department of Justice hasn't helped the company's reputation either.

Yet Facebook continues to push forward with efforts to make the most of its billions of members worldwide. Its recent acquisition of customer relationship management upstart Kustomer points to its plans to make its messaging capabilities more valuable to business customers and create new streams of revenue.

Look for Facebook and Apple to lead in 2021

For the Nasdaq to continue climbing next year, its most influential stocks will have to contribute to the upward momentum. Right now, investors are watching Apple and Facebook closely to see if they and their fellow FAANG stocks are likely to be able to get the job done in 2021 and beyond.

This article represents the opinion of the writer, who may disagree with the “official” recommendation position of a Motley Fool premium advisory service. We’re motley! Questioning an investing thesis -- even one of our own -- helps us all think critically about investing and make decisions that help us become smarter, happier, and richer.