High-growth and long-lasting business are almost a contradiction in terms. The faster they grow, the harder they fall. But what if you could find companies that actually combine heady growth rates with strong business models for the long term?

To find a few of these rare long-lasting growth tickers, we asked a few Motley Fool investors to share their best ideas. As it happens, all of them came back with companies from the networking industry. Read on to see why our panelists recommend buying and holding Palo Alto Networks (PANW 0.39%)ARRIS International (ARRS), and Cisco Systems (CSCO 0.43%) for the long run.

Many brightly colored networking cables, plugged into several switches shown at an angle.

Image source: Getty Images.

Imagine modern life without it

Chuck Saletta (Cisco Systems): Perhaps no company is more core to our modern, connected way of life than networking-titan Cisco Systems. By far the largest networking company in the world with about a 60% global share, Cisco Systems operates not just the networks, but much of the related connectivity technology that runs on it. That includes firewalls, cloud infrastructure, video conferencing, web-enabled meetings, IP telephony, analytics engines, security management, and more. 

Now that internet connectivity is available virtually everywhere in the world, Cisco Systems' massive growth from that initial onslaught of buildout has subsided. Still, between the need to upgrade infrastructure to handle continued internet traffic growth and the revenues from all its other products, the company still has a solid growth trajectory ahead.

Perhaps even better for investors, Cisco Systems' growth is available at a relatively modest price. Trading, as it does, at just above 15 times its expected forward earnings, the company's shares can practically be considered a bargain. Add to that a projected earnings growth of a bit above 9% annualized over the next five years, and you've got a reasonable anticipated growth trajectory available at a reasonable price.

There are few companies with both the product breadth and installed base of Cisco Systems, which gives it incredible current name recognition and the potential for strong cross-selling among current customers for a long time to come. That provides reason to believe Cisco's growth story may be around not just today and tomorrow, but for a long time to come.

Many blue network cables plugged into a rack of switches, alongside one red cable that also carries a padlock.

Image source: Getty Images.

The next-gen firewall leader

Leo Sun (Palo Alto Networks): The surge in data breaches over the past few years is bad news for companies and consumers, but great news for cybersecurity companies like Palo Alto Networks. Palo Alto provides next-gen firewalls for over 45,000 customers in more than 150 countries. That customer base includes over 85 of the Fortune 100 companies and more than 63% of the Global 2000.

That "best in breed" reputation has generated booming sales for Palo Alto. Its revenue rose 49% in fiscal 2016, 28% in 2017, and analysts expect 23% growth this year. Its earnings, on a non-GAAP basis, are expected to grow 26% this year.

Palo Alto keeps growing its business via a "land-and-expand" model, in which it secures firewall customers before upselling them additional services. One of its top priorities is to pivot customers toward its new hybrid cloud SaaS (software as a service) platform, which generates more subscription-based revenues.

Palo Alto has rallied about 216% over the past five years, but it still faces plenty of headwinds. The company isn't profitable on a GAAP basis (due to high stock-based compensation expenses), it faces growing competition from bigger companies like Cisco, and the stock isn't cheap at 37 times forward earnings.

Despite those challenges, I believe Palo Alto's dedicated customer base and its sound expansion strategies still make it a great growth stock to hold over the long term.

Huge growth at a deep discount

Anders Bylund (ARRIS International): From set-top boxes to internet-service gateways, Arris hardware likely can be found in your home. And even if you don't own something, your cable company probably does. The company is a storied innovator in the networking-hardware industry. Arris was in the early vanguard of important technologies such as high-definition digital TV signals, internet-based voice services, and hyper-efficient video-compression standards. This dominant player in the coaxial networking industry is going places.

Through a combination of organic growth and smart acquisitions, Arris grew its revenues nearly fivefold over the last five years. EBITDA profits ran neck and neck with the top-line surge, while free cash flows soared 770% higher.

Meanwhile, share prices only rose 66% higher. This was over a period where the S&P 500 market index nearly doubled in value.

The stock is trading at a deep discount these days. You can pick up Arris shares at less than nine times its trailing free cash flows today.

What's more, that rampant growth has legs. Analysts see Arris' earnings growth continuing to run at roughly 20% per year for the next five years. In other words, this growth stock should continue to run for years to come.