The Elder Scrolls IV: Oblivion Main Quest Guide

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Spies

This next quest is one of the easiest around. Speak to Juaffre and he'll
mention he fears the cloud ruler temple is being spied upon, and you're to
investigate.

He sends you to speak to either, or both, Captain Steffan right there at
cloud ruler, or to captain Burd down at Bruma. The first says you should
spy on the spies, and find out what they know and the second leads you
nearly straight to them.

Spying involves being at the place Steffan specifies before 7p.m. and
following the two spies back to their base, then killing them.
Alternatively, speak to Burd in Bruma to find there might be something
wrong with Jearl as she took a recent trip south.

This way involves picking the lock of jearls house. So you need a
lockpick but make sure no one sees you else you're violating the law.

You'll find Jearl and the other spy in the basement of Jearl's house, along
with their orders (lying on a small table there). Kill both and take the
orders back to Jauffre to finish the quest.