Bob Greifeld, chief executive of Nasdaq (NASDAQ:NDAQ), likes to battle. Despite announcing record results last week, he still boasted about how his exchange has helped in "driving the floor of the NYSE into the history books." Though Nasdaq has several battles to fight -- exchange upstart BATS is still biting into trading of Nasdaq-listed stocks -- Greifeld must also practice courtship skills. The acquisition of Sweden's OMX is progressing well. Yet Clara Furse, head of the London Stock Exchange (LSE), refuses to entertain Nasdaq as a suitor, despite its 30.5% share in her exchange.

First, the results. For the second quarter of 2007, Nasdaq reported record operating income of $99 million, and handsome operating margins of 49.8%. Net income for the quarter was $56.1 million. Net revenues were up 16% from the year-ago period, to $198.7 million.

Now to the battle. Nasdaq's share of Nasdaq-listed stocks appears to have stabilized. On the battle with NYSE Euronext (NYSE:NYX) for the trading of NYSE-listed stocks, Nasdaq inflicted severe wounds. Total NYSE-listed share volume increased from 22.7% in the second quarter of 2006 to 34.5% in the second quarter of 2007. And Nasdaq has no plans to stop fighting. Portal, Nasdaq's new marketplace for buying and selling private securities (so-called Rule 144A securities) is scheduled for release in August, and will face competition from single-dealer platforms, such as GSTrUe from Goldman Sachs (NYSE:GS). Similarly, Nasdaq is betting that decimalization in options trading will help its new options marketplace -- planned for release in the fourth quarter of this year -- and help to raise additional capital.

Weary of battle? Then think of courtship. The planned OMX merger makes fine progress, with both companies working on integration plans. Romancing the LSE remains rocky -- Nasdaq recently blocked a proposed share issue allowing LSE to fund its proposed acquisition of Borsa Italiana. No need for melancholy though -- investors can take heart from Nasdaq's refusal to overpay for the LSE, as well as the $332 million unrealized gain attached to Nasdaq's stake.

Nasdaq may be better at battle than courtship, but with its current execution and acquisition discipline, Robert Greifeld should be investors' favorite knight.

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Fool contributor John Finneran advises, trains, and writes on increasing the financial value of technology, especially, business cases. He does not own any of the shares mentioned.