On multiplicative functions resembling the Möbius function

For multiplicative functions f resembling the Möbius function μ  , we establish an upper bound for |∑n≤xf(n)| on much weaker assumptions on f which is comparable   with the upper bound for |M(x):=∑n≤xμ(n)| being obtained on assuming the Riemann Hypothesis and using the analytic properties of the generating function 1ζ(s).