The green stuff is cupric chloride, a byproduct of corrosion of the valve body or possible copper leachate in the water. Either way, it's typical of water leakage where the water is of low pH.
The white stuff (sometimes feels fibrous like cotton candy) is just efflorescence. This is from dissolved minerals in the water precipitating out as the leak drips, then dries and deposits miniscule quantities of calcium, sodium, etc on the valve body. You often see this where residual flux was left on a pipe and over time, condensation or outright leakage causes these buildups. It's always more pronounced at joints between dissimilar metals (due to galvanism).
Wearing gloves, as copper chlorides are toxic, you can remove them with full strength vinegar or dilute muriatic acid, lemon juice or even more flux and a bristle brush. Once it's cleaned up, repair the leak or tighten the packing gland on the valve stem. Then when all done, just liberally apply a paste of baking soda and water. It will neutralize the flux and retard further reaction (if it's condensation related). It would be wise to have your water tested for acidity. If you have highly acidic water, it can cause the same problem or just dissolve pipes outright.