<p>We study a class of abstract evolution equations driven by singular memory laws that combine a local time derivative with a nonlocal convolution term. This framework includes, as particular or limiting cases, the first-order abstract Cauchy problem, abstract Basset equations, multi-term and distributed-order fractional models, and purely nonlocal diffusion equations. Our starting point is the constitutive memory law itself, rather than a Volterra kernel prescribed in advance. We show that each singular memory law in this class determines a unique canonical locally integrable kernel, and that the original problem is therefore equivalent to an abstract Volterra equation governed by this kernel and by an associated Laplace symbol. We then establish transfer principles from the original memory law to the canonical kernel, obtaining consequences for complete monotonicity, regularity, and sectoriality that lead to generation criteria for the corresponding resolvent families. Finally, we analyze singular limits connecting the local and purely nonlocal regimes and discuss canonical examples arising from fractional, Basset-type, and distributed-order models. In this way, the paper provides a unified operator-theoretic framework for a broad family of evolution equations with memory.</p>