The documentation says that URL does not have to have quotes (http://docs.oracle.com/javafx/2/api/javafx/scene/doc-files/cssref.html#typeuri) but when entering a valid property value like this:

.bla {
-fx-background-image: url(http://www.bestsolution.at/test.png);
}

into a css file it fails with:

J?n 16, 2013 10:14:30 AM com.sun.javafx.css.parser.CSSParser term
WARNING: CSS Error parsing file:/Users/tomschindl/Documents/e4_workspaces/efxclipse/rt/bin/tests/my.css: Unexpected token ':' at [12,31]
J?n 16, 2013 10:14:30 AM com.sun.javafx.css.parser.CSSParser term
WARNING: CSS Error parsing file:/Users/tomschindl/Documents/e4_workspaces/efxclipse/rt/bin/tests/my.css: Unexpected token ':' at [12,31]
J?n 16, 2013 10:14:30 AM com.sun.javafx.css.parser.CSSParser reportException
WARNING: Please report java.lang.NullPointerException at:
com.sun.javafx.css.parser.CSSParser.term(CSSParser.java:4220)
com.sun.javafx.css.parser.CSSParser.expr(CSSParser.java:4118)
com.sun.javafx.css.parser.CSSParser.declaration(CSSParser.java:4089)
com.sun.javafx.css.parser.CSSParser.declarations(CSSParser.java:4007)
com.sun.javafx.css.parser.CSSParser.parse(CSSParser.java:3628)
com.sun.javafx.css.parser.CSSParser.parse(CSSParser.java:255)
com.sun.javafx.css.parser.CSSParser.parse(CSSParser.java:243)

url is a special construct and not a function (see http://www.w3.org/TR/CSS21/grammar.html) where url is speced. If the CSS-Parser is not able to support this construct it should at least not doc the not supported format.