We define the flatness and quasi-flatness problems in cosmological models. Weseek solutions to both problems in homogeneous and isotropic Brans-Dickecosmologies with varying speed of light. We formulate this theory and findperturbative, non-perturbative, and asymptotic solutions using both numericaland analytical methods. For a particular range of variations of the speed oflight the flatness problem can be solved. Under other conditions there exists alate-time attractor with a constant value of \Omega that is smaller than, butof order, unity. Thus these theories may solve the quasi-flatness problem, aconsiderably more challenging problem than the flatness problem. We alsodiscuss the related \Lambda and quasi-\Lambda problem in these theories. Weconclude with an appraisal of the difficulties these theories may face.
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