How to add multiple gradients in an offset path like this?

[Guest]

So, I want my logo to be have multiple gradients like this. I tried but wasn't able to do so. Any help is appreciated.

[Monika Gause]

And this is your design?

I'm not quite sure what you want to achieve and what youe base objects are.

[Jacob Bugge]

Usa,

Without entering any considerations about suitability for a logo:

As ( (mis)understand it, you can:

1) Start out with your black line letter shapes as a Group of Stroke Nofill paths with Round Cap and Round Join on top of the original background with the wavy colour transitions;

2) With the Group selected, in the Appearance panel Add New Stroke, then drag the New Stroke down below the original black Stroke and give it the desired Stroke Weight to appear on both sides and at the ends of each original path, and make it white so you can see clearly what you are doing, then select only the white Stroke in the Appearance panel and set its Opacity to 0% in the Transparency panel; it will (literally) disappear but there is no need to worry;

3) Create a rectangle with the same size and position as the background from 1) and give it the desired vertical linear gradient, the upper and lower parts being of uniform colour (the (colour transition of the) Gradient starting at more than 0% and ending at less than 100%), then drag it below the background;

4) Select the Group of paths from 2) and also the original background with the wavy colour transitions from 1) and Group them; be careful to keep the rectangle with the gradient out of the Group;

5) In the Transparency panel tick Knockout Group.

This ought to make the transparent (formerly white) new Stroke knock out the underlying parts of the original background so the gradient of the bottommost rectabgle shows through and appears as if the new Stroke round the black paths has the vertical gradient.

[Anna Lander]

as far as I can see the example contains gradient fills, not strokes, So the easiest way to repeat this effect is 

1. take the elements of your logo and create an Offset Path (Object > Path > Offset Path). Set the offset value as you need. Ungroup all.

2. Select the Offset Psth and set the gradient as you want. You can it the same for all shapes or tweak it using the Gradient tool.