Sonny 1950:

Fear not, your trees are in no danger. The sticky stuff is honeydew from yellow aphids. You should be able to see the aphids on the underside of leaves, but they could be high in the tree. Many people experience this problem with pecans and complain when their car turns into a lolly pop. It's not that serious although heavy numbers can reduce pecan yield and quality.

A more serious aphid is the black aphid. It can partially defoliate the tree. These usually occur in small numbers on leaves in the lower canopy. If you see leaves with segments of the leaf turning yellow, you may have this pest. Commercial growers spray for this one.

For what it's worth the "nut" part of my handle references the 20 yrs I spent in pecan variety development for Texas A&M Univ.

The Fruitnut

Hose 'em off.

Would these be black aphids? The leaves are sticky but there is no yellow residue