While conducting approaches to LFI in actual IMC a BE20 at 2100 FT took evasive action in response to a TCAS TA target.

Narrative

I was vectored on a 090 heading to intercept the TACAN 08 approach course to Langley AFB (LFI) and was cleared for the approach. I was cleared to descend to 2000 FT to intercept. Norfolk Approach warned of VFR traffic ahead and to the right. My TCAS showed them initially at 1200 FT and about 3 or 4 miles ahead. As the target appeared to get closer I noticed the altitude separation was now decreasing. I slowed my descent and leveled at 2100 FT. I told the Controller that I was in solid IMC conditions and he stated that the VFR target appeared to be closing on me. TCAS showed the other aircraft rapidly climbing and at that moment I got a TA warning and estimated that if I continued there was potential for a collision. I estimate my vertical separation to have been about 150 FT based on the TCAS readouts that I was receiving. I immediately climbed to 2900 FT in a climbing right turn and notified the Controller of my deviation. I was still in IMC conditions and never visually saw the traffic. The Controller recleared me for the TACAN 08 Approach to intercept at 2000 FT which I then proceeded to do. I broke out of the clouds at about 1600 FT. I had originally entered the solid undercast layer at about 3400 FT on my descent. I continued an uneventful approach and landing at LFI. It is my opinion that the other aircraft could not have been operating legally under VFR with the weather conditions that were in the vicinity of the incident.