Research from ChangeWave shows that Research In Motion (NASDAQ: RIMM)'s BlackBerry still holds the lead in the smartphone business, but Apple (NASDAQ: AAPL) is marking important inroads. Palm (NASDAQ: PALM) continues to be in a bad spot.

The data is from a check of almost 4,000 consumers interviewed from March 17 to March 24. According to the research, the RIM BlackBerry maintains its huge lead among consumers with 42% of the market while second place Palm continues a two-year decline in its share and now holds 16% . This was the seventh-consecutive ChangeWave survey in which Palm's market share has dropped.

Apple's market share is now up to 9%, extraordinary given the short time the iPhone has been in the market.

In terms of people being "very satisfied" with their handsets, the poll shows Apple with a rating of 79%. RIMM comes in at 54% and Palm at 22%. Of those planning to buy a smartphone in the next 90 days, 35% plan to buy the Apple product.

Research In Motion appears to be holding its own in what is a fast-growing market for smartphones. The iPhone continues to be a once-in-generation product. Palm is toast.

Douglas A. McIntyre is an editor at 247wallst.com.