Abstraet. In this paper we presentan overview of the radio-frequency muon spin resonance (RF~tSR) teehnique, ah analogue to continuous-wave NMR, and an introduction to time-integral (TI) and timedifferential (TD) RF~SR on muons in diamagnetic or in paramagnetic environments. The general form of the resonance line for TI-RFp.SR as well as the expression for the time-dependence of the longitudinal muon spin polarization at resonance ate given. Since RFIzSR does not require phase coherente of the muon spin ensemble, this teclmique allows us to investigate muon species that ate generated by transitions from, or in the course of reactions of, a precursor muon species even ir in transverse-field (TF) ~tSR measurements the signal is lost due to dephasing. This ability of RF~tSR is clearly demonstrated by measurements on doped Si. In this example, at low temperatures, a very pronounced signal from a muon species in diamagnetic environment has been found in RF~tSR measurements, whereas in TF~tSR experiments only a very small signal from muons in diamagnetic environment could be detected anda large fraction of the implanted muons escaped detection. These findings could be interpreted in terms of the delayed formation of a diamagnetic muonium-dopant complex, and, due to the large diamagnetic RFp.SR signal, the RFp.SR teclmique is a unique tool to study how the variation of parameters and experimental eonditions suela as illumination affects formation and behavior of these complexes. First results obtained on illuminated boron doped Si are reported. However, as illustrated by the example of experiments on the muonated radical in solid C60, results from conventional TI-RFbtSR eannot always be interpreted unambiguously sinee different parameters, namely the fraction of muons forming the investigated muon species, the longitudinal and the transverse relaxation rates, have similar effects on height and shape of the RFp.SR resonance line. These ambiguities, however, may be resolved by collecting time-differential data. With this extension RF~tSR becomes a very powerful complementary method to TF~tSR in the studies of dynamic effects.