How to account for both between-subjects and within-subjects covariables?

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I have a data set I'm trying to analyze and I can't figure out how to include the two different kinds of covariables in my analysis.

Without the covariables, the analysis isn't too complicated. It's a repeated measures design. Every subject took test A and test B. Half took them in one order and half took them in the other order. But I have several covariables that I'd like to include. I actually have way too many covariables, but I've narrowed the list down beforehand. That still leaves two different types of covariables to deal with though. A few were measured along with each individual test, and a few were measured before or after and apply to each subject.

My question is, what analysis technique should I be using to answer the final question, "are the results of test A and test B significantly different?" and how do I include the two different kinds of covariables in that?