From Introduction to Local Minimization:

With Method -> Automatic, the Wolfram Language uses the quasi-Newton method unless the problem is structurally a sum of squares, in which case the Levenberg-Marquardt variant of the Gauss-Newton method is used.

To confirm, I use the first example in FindFit >> Options >> Method and compare the output for various settings for the Method option:

Possible settings for Method include "ConjugateGradient", "Gradient", "LevenbergMarquardt", "Newton", "NMinimize", and "QuasiNewton", with the default being Automatic.

model = a Exp[-b (x - c)^2] + d Sin[ω x + ϕ];
data = Table[{x, model /. {a -> 2, b -> 1, c -> 0, d -> 2, ω -> 0.67, ϕ -> 0.1}}, 
           {x, -5, 5, .1}] + RandomReal[.25, 101];

methods = {Automatic, "ConjugateGradient", "Gradient", "LevenbergMarquardt",
           "Newton", "NMinimize", "QuasiNewton"};

Grid[Partition[Labeled[Quiet@NonlinearModelFit[data, model, {a, b, c, d, ω, ϕ}, 
        x, Method -> #]["ParameterTable"], #, Top] & /@ methods, 3], Spacings -> {5, 5}]

From Introduction to Local Minimization:

With Method -> Automatic, the Wolfram Language uses the quasi-Newton method unless the problem is structurally a sum of squares, in which case the Levenberg-Marquardt variant of the Gauss-Newton method is used.

To confirm, I use the first example in FindFit >> Options >> Method and compare the output for various settings for the Method option:

Possible settings for Method include "ConjugateGradient", "Gradient", "LevenbergMarquardt", "Newton", "NMinimize", and "QuasiNewton", with the default being Automatic.

model = a Exp[-b (x - c)^2] + d Sin[ω x + ϕ];
data = Table[{x, model /. {a -> 2, b -> 1, c -> 0, d -> 2, ω -> 0.67, ϕ -> 0.1}}, 
           {x, -5, 5, .1}] + RandomReal[.25, 101];

methods = {Automatic, "ConjugateGradient", "Gradient", "LevenbergMarquardt",
           "Newton", "NMinimize", "QuasiNewton"};

nlms = Quiet@ NonlinearModelFit[data, model, {a, b, c, d, ω, ϕ}, x, 
                 Method -> #]["ParameterTable"] & /@ methods; 
Grid[Partition[Labeled[#, #2, Top] & @@@ Transpose[{nlms, methods}], 3], Spacings -> {5, 5}]

From Introduction to Local Minimization:

With Method -> Automatic, the Wolfram Language uses the quasi-Newton method unless the problem is structurally a sum of squares, in which case the Levenberg-Marquardt variant of the Gauss-Newton method is used.

To confirm, I use the first example in FindFit >> Options >> Method and compare the output for various settings for the Method option:

Possible settings for Method include "ConjugateGradient", "Gradient", "LevenbergMarquardt", "Newton", "NMinimize", and "QuasiNewton", with the default being Automatic.

model = a Exp[-b (x - c)^2] + d Sin[ω x + ϕ];
data = Table[{x, model /. {a -> 2, b -> 1, c -> 0, d -> 2, ω -> 0.67, ϕ -> 0.1}}, 
           {x, -5, 5, .1}] + RandomReal[.25, 101];

methods = {Automatic, "ConjugateGradient", "Gradient", "LevenbergMarquardt",
           "Newton", "NMinimize", "QuasiNewton"};

Grid[Partition[Labeled[Quiet@NonlinearModelFit[data, model, {a, b, c, d, ω, ϕ}, 
        x, Method -> #]["ParameterTable"], #, Top] & /@ methods, 3], Spacings -> {5, 5}]

From Introduction to Local Minimization:

With Method -> Automatic, the Wolfram Language uses the quasi-Newton method unless the problem is structurally a sum of squares, in which case the Levenberg-Marquardt variant of the Gauss-Newton method is used.

To confirm, I use the first example in FindFit >> Options >> Method and compare the output for various settings for the Method option:

Possible settings for Method include "ConjugateGradient", "Gradient", "LevenbergMarquardt", "Newton", "NMinimize", and "QuasiNewton", with the default being Automatic.

model = a Exp[-b (x - c)^2] + d Sin[ω x + ϕ];
data = Table[{x, model /. {a -> 2, b -> 1, c -> 0, d -> 2, ω -> 0.67, ϕ -> 0.1}}, 
           {x, -5, 5, .1}] + RandomReal[.25, 101];

methods = {Automatic, "ConjugateGradient", "Gradient", "LevenbergMarquardt",
           "Newton", "NMinimize", "QuasiNewton"};

Grid[Partition[Labeled[Quiet@NonlinearModelFit[data, model, {a, b, c, d, ω, ϕ}, 
        x, Method -> #]["ParameterTable"], #, Top] & /@ methods, 3], Spacings -> {5, 5}]