The ab plane optical spectra of two single crystals of La(2-x)Sr(x)Cu(4), one overdoped and one underdoped, were investigated. We observe a gap-like depression of the effective scattering rate below 700 cm(-1) in both systems. This feature persists up to 300 K in the underdoped sample with the concentration of Sr x=0.14 but loses prominance at temperatures above 300 K in the overdoped regime (x=0.22). Below 700 cm(-1) the scattering rate is temperature dependent and superlinear in frequency for both samples. Above this frequency the effective scattering rate becomes linear in frequency and is temperature independent in the case of the underdoped La(1.86)Sr(0.14)CuO(4) up to 300 K. On the other hand, the overdoped La(1.76)Sr(0.22)CuO(4) shows a scattering rate temperature dependence above 700 cm(-1) at all temperatures. This behaviour of the frequency and temperature dependent scattering rates is a signature of a pseudogap state in other HTSC materials and suggests that both the under and overdoped single-layer HTSC systems Ls(2-x)Sr(x)CuO(4) have a pseudogap at temperatures exceeding 300 K.