ASX healthcare shares offer some of the best opportunities in my opinion, and December is shaping up to be a pivotal month for two of the most promising stocks: ResMed Inc (ASX: RMD) and CSL Ltd (ASX: CSL).

Both healthcare players have a good set of tailwinds behind them and are rated highly by brokers.

ResMed currently fetches $37.95 apiece, whereas CSL trades at $281.70 per share at the time of writing. Here's why I think these two ASX healthcare shares standout in December.

ResMed shares continue ascent

ResMed has had a stellar run in 2024, with shares up 50% this year to date. But experts say there is plenty of fuel left in the tank.

In fact, several analysts believe the ASX healthcare share is positioned for growth into the future.

The company's revenues were up 12% in FY24 to reach $4.7 billion, with free cash flow hitting an impressive $1.3 billion.

That's 27.7 cents of free cash flow underneath every dollar of revenue. It's no wonder everyone is talking about ResMed shares.

Growth was underscored by demand for its sleep apnoea products, and a 28% rise in patient enrolment for its 'myAir' app.

But it's the future that counts for investors.

According to CommSec, looking ahead, consensus projects ResMed to grow earnings by 20% from FY25 to FY27. The company could earn $1.54 per share by then.

Ord Minnett was bullish on ResMed's recent quarterly numbers. The broker sees continued growth in revenues and rates the ASX healthcare share a buy with a revised $40.05 price target.

CSL: Standout ASX healthcare share this December

CSL is one of Australia's greatest health company stories, transforming into a global biotech behemoth with a market capitalisation of $136.40 billion at the time of writing.

Shares have drifted lower this year and are down 2% in 2024 in a world where the broad markets have rallied.

Despite this, the ASX healthcare share's fundamentals remain rock-solid in my view. Plus, several brokers reckon current prices are an attractive entry point.

Bell Potter analysts recently highlighted CSL's positive earnings outlook and the start of a "margin recovery phase".

This should "[drive] above-market earnings growth over the next few years", the broker says

Bell Potter has set a price target of $345 on CSL shares, implying a potential upside of 22% from the ASX healthcare share's current price.

Foolish takeout

According to experts, both of these ASX healthcare shares have what it takes to deliver solid gains over the coming 12 months.

In the last 12 months, CSL is up 7%, whereas ResMed has climbed 53%.