One of us has recently found experimental evidence for unconventional superconductivity in a newly synthesized three-dimensional nearly antiferromagnetic metal, LaAg1−xMnx with five fold increase in TC to ~5 K. All the bulk measurements indicate that the antiferromagnetic spin-fluctuation-mediated pairing may have a direct bearing on this phenomenon. Compared to the heavy-fermion systems, the superconducting transition temperature is nearly 10 times higher, superconductivity is robust against impurities and the specific-heat anomaly associated with the superconducting transition is extremely weak, or even absent. We therefore propose to investigate these alloys using microscopic probe such as μSR, using MUSR spectrometer, that gives direct information on the superconducting properties as well as on the magnetic spin fluctuations.