We present measurements of the penetration depth lambda(T) in YBa2(Cu1
-xNix)3O7 (x = .04,.06) and pure YBa2Cu3O7 films obtained from the T d
ependence of the mutual inductance of two coaxial coils on opposite si
des of the films. lambda(0) increases by a factor of 5 with 4 % Ni and
a factor of 10 with 6 % Ni. The data are well fitted by the function
lambda(T) = lambda(0)/(1-T2/T(c)2)1/2 over the entire temperature rang
e from 7K to T(c), implying at low temperatures lambda(T) almost-equal
-to lambda(0)(1+alphaT2/T(c)2) with a coefficient a that is independen
t of nickel concentration.