In the earlier joint work [3], we introduced the weak Kahler-Ricci flow for various geometric motivations. In this current work, we take further consideration on setting up the weak flow by allowing the initial class to be not necessary Kahler. It’s shown that the construction is compatible with the earlier construction in Kahler case. We also discuss the convergence as t→ 0+ which is of great interest in this topic, and provide related motivation. 1. Motivation and set-up of weak flow The Kahler-Ricci flow, the complex version of Ricci flow, has been under intensive study over the last twenty some years. In [18] and more recently [17], G. Tian proposed the intriguing program of constructing globally existing (weak) KahlerRicci flow with canonical (singular) limit at time infinity and applying it to the study of algebraic manifolds (and even Kahler manifolds in general). It can be viewed as the analytic version of the famous Minimal Model Program in algebraic geometry. In general, people should expect the classic smooth Kahler-Ricci flow to encounter singularity at some finite time which is completely decided by cohomology information according to the optimal existence result in [20]. Just as what people have been doing and had successes in cases for Ricci flow, surgeries for the underlying manifold should be expected. For the Kahler-Ricci flow, we naturally expect the surgery to have flavours from algebraic geometry. A simple example would be surfaces of general type. One only needs the blowingdown of (−1)-curves when applying the general construction at the end of [3] to push the flow through the finite time of singularities, where the measure restriction is actually not so involved as explained later in Example 4.4. The degenerate class at the singularity time would become Kahler for the new manifold because those (−1)-curves causing the cohomology degeneration would eventually been crushed to points. Things can get significantly more complicated for higher dimension. For example, a standard procedure called flip is introduced in the algebraic geometry context, which is of great importance for the business about the algebraic Minimal Model Program. Simply speaking, one needs to blow up the manifold and then perform a different blowing-down process. Naturally, we should expect the transformation of the degenerate class is still not Kahler. In this note, we confirm that this is not a problem under the assumption that formally the Kahler-Ricci flow is instantly Date: received on January 6, 2012 and accepted on August 22, 2012. 2010 Mathematics Subject Classification. Primary 53C44; Secondary 14E30, 58J35.