Anycast is a point to point flow of packets for obtaining services or sending data to one of a multitude of destinations that share one address. To meet needs of real time and multimedia applications, anycast routing in Mobile Ad hoc Networks (MANETs) must provide faster service with better Quality of Service (QoS). This paper proposes an Adaptive Neuro-Fuzzy Inference System (ANFIS) based multiple QoS constrained anycast routing in MANETs by using a set of static and mobile agents. Three types of agents are used in the scheme: static anycast manager agent, static optimization agent, and mobile anycast route creation agent. The scheme operates in the following steps. (1) Optimization agent at the client optimizes membership functions for bandwidth, link delay and packet loss rate to develop Fuzzy Inference System (FIS) by using ANFIS. (2) Anycast route creation agents are employed by the client to explore multiple paths from source (client) to all anycast members (servers) through intermediate nodes. These agents gather intermediate node's information such as available bandwidth, link delay, residual battery power, and stability of anycast servers. The information is passed on to the client. (3) Anycast manager agent at the client performs finding QoS factor by using optimized FIS for every path, and selects QoS anycast path based on QoS and server stability factor, and (4) Anycast route creation agent is also employed for maintaining the QoS path in the event of node/link failures. The simulation results demonstrate reduction in end-to-end delay and control overhead, improvement in packet delivery ratio and path success ratio, as compared to shortcut tree based anycast routing (SATR) in MANETs.