Stocks will continue to push upward before a final break in the next few months, serving as the last throes of what will be the longest bull market in history.

That is according to forecasts by technical analysts at ING, commenting on the hitting record levels this week.

The 500-company benchmark index advanced 0.2 percent to close at 2,857.05 on Monday, and is now just under 0.6 percent from its record, reached in late January of this year. The fact that the market recently closed the downside January gap between 2,838 and 2,852 is "encouraging," said Roelof-Jan van den Akker, ING's senior technical analyst.

"That's telling me that we should expect a break above the upper end of this market, challenging to new all-time highs above the horizontal resistance at 2,875 in the end." The January record was 2,872.87.

"I believe a break above 2,875 would attract buyers, of course; that's a new phase that would suggest a resumption of this longer term uptrend," van den Akker told CNBC's "Squawk Box Europe" on Tuesday. A break above the 2,795 level a few months ago completed what the analyst called a bottle formation, whose size suggests a target of around 3,150 to 3,200 — "that's in line with our longer-term price target coming in around 3,130."

On Tuesday, the S&P 500 will equal the longest U.S. bull market since World War II; on August 22, it will be the longest in history at nearly 3,500 days. Since its bear market low of 676 on March 9, 2009, its risen more than 320 percent, with major market movers like Netflix and Ulta Beauty up more than an eye-watering 5,500 percent.

As the S&P is a market cap weighted index, the bigger the market cap, the more it can move markets. Other companies making up some of the index's big gains are Amazon, which accounted for 4.1 percent of gains since 2009, followed by Microsoft, J.P. Morgan, General Electric and Wells Fargo.