The magnetic properties of La1.85Sr0.15CuO4 doped with Ni was investigated in the field up to 5 T and in the temperature range from 2 K to 400 K using both dc and ac techniques. For Ni content larger than 0.05 the system exhibits irreversibility of low-field susceptibility χ(T ) below a certain temperature depending on y and a cusp at T g in χ(T ) measured after zero-field cooling. The decay of remnant magnetization below T g with time is described by a stretched-exponential function. In accordance with scaling theory, all the χ(T ) data for y = 0.50 sample taken in the vicinity of T g at different fields collapse onto two separate curves when plotted as q|t| −β vs. B 2 |t| −β−γ , where q is the spin-glass order parameter, t = (T − T g )/T g , and β and γ are the critical exponents. All these features taken together reveal existence of spin-glass phase below T g . Variation of T g with y is linear below y = 0.25 and T g extrapolates to 0 K for y → 0 what strongly suggests that spin-glass phase extends into superconducting region of the phase diagram.