Let \(U(t,x)\) be a solution of the stochastic partial differential equation \(U_ t=U_{xx}+U^ \gamma \dot W\), where \(\gamma\geq 1\), \(\dot W\) is a 2-parameter white noise. If \(U(0,x)\) is bounded, nonnegative, with compact support and not identically \(0\), then with probability 1, \(U(t,x)>0\) for all \(t>0\), \(x\in R\).