In this paper we present new results on asymptotic consensus for continuous-time nonlinear time varying networks. A key feature in the following is that the monotonicity property (i.e. cooperativity) is not required, unlike most of existing literature on the subject. Additionally, we extend the use of a 'State Frozen' concept [16] and integral connectivity to this non-trivial scenario, and give condition for consensus with the additional merit to be frozen in state variables and therefore of simpler verification. Finally, we give an estimate of the exponential rate of convergence towards the agreement manifold.