Using　compactly　supported　wavelets,　Gine　and　Nickl　[Uniform　limit　theorems　for　wavelet　density　estimators,　Ann.　Probab.　37(4)　(2009)　1605-1646]　obtain　the　optimal　strong　L-infinity(R)　convergence　rates　of　wavelet　estimators　for　a　fixed　noise-free　density　function.　They　also　study　the　same　problem　by　spline　wavelets　[Adaptive　estimation　of　a　distribution　function　and　its　density　in　sup-norm　loss　by　wavelet　and　spline　projections,　Bernoulli　16(4)　(2010)　1137-1163].　This　paper　considers　the　strong　L-p(R)　(1　＜=　p　＜=　infinity)　convergence　of　wavelet　deconvolution　density　estimators.　We　first　show　the　strong　L-p　consistency　of　our　wavelet　estimator,　when　the　Fourier　transform　of　the　noise　density　has　no　zeros.　Then　strong　L-p　convergence　rates　are　provided,　when　the　noises　are　severely　and　moderately　ill-posed.　In　particular,　for　moderately　ill-posed　noises　and　p　=　infinity,　our　convergence　rate　is　close　to　Gine　and　Nickl＇s.