Mostly hydrogen, with some helium and methane and a small amount of water vapour

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Neptune's thick atmosphere consist of 74% hydrogen, 25% helium and about 1% methane. The atmosphere merges into the planet's mantle. Neptune's atmosphere has icy clouds and enormous storms. These features change rapidly because of tremendous winds that whip around the planet. Neptune has the fastest winds in our Solar System. Icy particles of methane in the outer parts of its atmosphere give Neptune its deep blue color; methane absorbs red light. http://www.enchantedlearning.com/subjects/astronomy/planets/neptune/atmosphere.shtml Neptune's atmosphere is made up of hydrogen, helium, and methane. Like Earth's atmosphere, Neptune's has clouds and storm systems that revolve around the planet, but with wind speeds of 300 m/sec (700 mi/hr), and clouds of frozen methane. http://www.nasm.si.edu/research/ceps/etp/neptune/nept_atmos.html Just like the other gas giant planets in the outer solar system (Jupiter, Saturn, and Uranus), Neptune's atmosphere comprises mostly molecular hydrogen 84% (H2) and helium 14% (He). Like Uranus, but unlike Jupiter and Saturn, Neptune abounds in methane 2% (CH4). The prevalence of methane correlates with the internal composition of these planets. Neptune appears blue in color, and bands of clouds cross its atmosphere along the planet's parallels. The blue color results from the presence of methane vapor: methane efficiently absorbs the red wavelengths of the Sun's light, letting only the blue wavelengths through to the thick cloud deck covering the planet; these are the wavelengths that are then reflected back to our eye. Calculations lead us to hypothesize the abundance of other compounds in Neptune's atmosphere as well. But these compounds, e.g., ammonia (NH3) and water (H2O), have never in fact been found on the planet. One possible explanation for this, supported by computer models of the planet's atmosphere, is that these compounds condense into clouds at temperatures and pressures corresponding to those of Neptune's lowest atmospheric levels; thus no vapors of these compounds escape to the upper atmosphere, where scientists take their measurements. http://www.sparknotes.com/astronomy/neptune/section3.rhtml Like the other giant planets, Neptune's outer atmosphere is composed predominantly of hydrogen and helium. Near the one-bar pressure level in the atmosphere, these two gases contribute nearly 98 percent of the atmospheric molecules. Most of the remaining molecules consist of methane gas. Hydrogen and helium are nearly invisible, but methane strongly absorbs red light. Sunlight reflected off Neptune's clouds therefore exits the atmosphere with most of its red colours removed and so has a bluish cast. Although Uranus's blue-green colour is also the result of atmospheric methane, Neptune's colour is a more vivid, brighter blue, presumably an effect of the presence of an unidentified atmospheric gas. http://original.britannica.com/eb/article-54299/Neptune