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Spectral asymptotics of a tensor product of compact operators in Hilbertspace with known marginal asymptotics is studied. Methods of A. Karol', A.Nazarov and Ya. Nikitin (Trans. AMS, 2008) are generalized for operators withalmost regular marginal asymptotics. In many (but not all) cases it is shown,that tensor product has almost regular asymptotics as well. Obtained resultsare then applied to the theory of small ball probabilities of Gaussian randomfields.

On spectral asymptotics of the tensor product of operators with almost regular marginal asymptotics