Fundamental limitations on estimation accuracy are well known and include a variety of lower bounds including the celebrated Cramer Rao Lower Bound. However, similar theoretical limitations on resolution have not yet been presented. We exploit results from detection theory for deriving fundamental limitations on resolution. In this paper we discuss the resolution of two zero mean complex random Gaussian signals with a general and predefined covariance matrix observed with additive white Gaussian noise. The results are not based on any specific resolution technique and thus hold for any method and any resolution success rate. The theoretical limit is a simple expression of the observation interval, the user's pre-specified resolution success rate and the second derivative of the covariance matrix. We apply the results to the bearing resolution of two emitters with closely spaced direction of arrival impinging on an array of sensors. The derived limits are verified experimentally by model order selection methods such as the Akaike Information Criterion and the Minimum Description Length.