Although it is hard to tell from the picture, I would say they are aphids. The sticky stuff is honey dew they produce and the black is a mold that grows on the honey dew. The cheapest and safest control method is blasting them off with a strong stream of water from the hose. You will have to repeat this every couple of days for a wk or two and then as needed.

Thanks, I think that's right. What about the ladybugs, won't I be harming them if I blast them with the hose? BTW, I tried to send 2 photos, the 2nd one showing tbe buggers on my finger, but was unsuccessful.

The Ladybugs will fly away and return to feed on the remaining aphids.

Many thanks! As soon as this wind dies down I'll put my hose to those aphids.

These sticky bugs have destroyed my spanish broom eaten all blooms and are killing the bush

what is the solution

Aphids don't eat plants. They don't have mouths capable of chewing. What they do is suck the sap causing distortion and, if it's a heavy infestation, damage or death. If something is genuinely eating your broom it doesn't sound like aphids. Do you have a picture?